TSTP Solution File: LAT307+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT307+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:55 EDT 2022
% Result : Theorem 22.23s 14.25s
% Output : Proof 22.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : LAT307+1 : TPTP v8.1.0. Released v3.4.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n011.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Sep 1 13:49:12 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.15/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.30 Usage: tptp [options] [-file:]file
% 0.15/0.30 -h, -? prints this message.
% 0.15/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.30 -m, -model generate model.
% 0.15/0.30 -p, -proof generate proof.
% 0.15/0.30 -c, -core generate unsat core of named formulas.
% 0.15/0.30 -st, -statistics display statistics.
% 0.15/0.30 -t:timeout set timeout (in second).
% 0.15/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.30 -<param>:<value> configuration parameter and value.
% 0.15/0.30 -o:<output-file> file to place output in.
% 22.23/14.25 % SZS status Theorem
% 22.23/14.25 % SZS output start Proof
% 22.23/14.25 tff(v1_filter_0_type, type, (
% 22.23/14.25 v1_filter_0: ( $i * $i ) > $o)).
% 22.23/14.25 tff(k1_lattice2_type, type, (
% 22.23/14.25 k1_lattice2: $i > $i)).
% 22.23/14.25 tff(tptp_fun_A_0_type, type, (
% 22.23/14.25 tptp_fun_A_0: $i)).
% 22.23/14.25 tff(k15_filter_2_type, type, (
% 22.23/14.25 k15_filter_2: ( $i * $i ) > $i)).
% 22.23/14.25 tff(tptp_fun_C_27_type, type, (
% 22.23/14.25 tptp_fun_C_27: ( $i * $i ) > $i)).
% 22.23/14.25 tff(g3_lattices_type, type, (
% 22.23/14.25 g3_lattices: ( $i * $i * $i ) > $i)).
% 22.23/14.25 tff(u2_lattices_type, type, (
% 22.23/14.25 u2_lattices: $i > $i)).
% 22.23/14.25 tff(u1_lattices_type, type, (
% 22.23/14.25 u1_lattices: $i > $i)).
% 22.23/14.25 tff(u1_struct_0_type, type, (
% 22.23/14.25 u1_struct_0: $i > $i)).
% 22.23/14.25 tff(k7_filter_2_type, type, (
% 22.23/14.25 k7_filter_2: ( $i * $i ) > $i)).
% 22.23/14.25 tff(tptp_fun_B_1_type, type, (
% 22.23/14.25 tptp_fun_B_1: $i)).
% 22.23/14.25 tff(l3_lattices_type, type, (
% 22.23/14.25 l3_lattices: $i > $o)).
% 22.23/14.25 tff(v10_lattices_type, type, (
% 22.23/14.25 v10_lattices: $i > $o)).
% 22.23/14.25 tff(v3_struct_0_type, type, (
% 22.23/14.25 v3_struct_0: $i > $o)).
% 22.23/14.25 tff(v14_lattices_type, type, (
% 22.23/14.25 v14_lattices: $i > $o)).
% 22.23/14.25 tff(r2_filter_2_type, type, (
% 22.23/14.25 r2_filter_2: ( $i * $i ) > $o)).
% 22.23/14.25 tff(r1_tarski_type, type, (
% 22.23/14.25 r1_tarski: ( $i * $i ) > $o)).
% 22.23/14.25 tff(m2_filter_2_type, type, (
% 22.23/14.25 m2_filter_2: ( $i * $i ) > $o)).
% 22.23/14.25 tff(m1_subset_1_type, type, (
% 22.23/14.25 m1_subset_1: ( $i * $i ) > $o)).
% 22.23/14.25 tff(k1_zfmisc_1_type, type, (
% 22.23/14.25 k1_zfmisc_1: $i > $i)).
% 22.23/14.25 tff(v3_lattices_type, type, (
% 22.23/14.25 v3_lattices: $i > $o)).
% 22.23/14.25 tff(m1_relset_1_type, type, (
% 22.23/14.25 m1_relset_1: ( $i * $i * $i ) > $o)).
% 22.23/14.25 tff(k2_zfmisc_1_type, type, (
% 22.23/14.25 k2_zfmisc_1: ( $i * $i ) > $i)).
% 22.23/14.25 tff(m2_relset_1_type, type, (
% 22.23/14.25 m2_relset_1: ( $i * $i * $i ) > $o)).
% 22.23/14.25 tff(v1_funct_2_type, type, (
% 22.23/14.25 v1_funct_2: ( $i * $i * $i ) > $o)).
% 22.23/14.25 tff(v1_funct_1_type, type, (
% 22.23/14.25 v1_funct_1: $i > $o)).
% 22.23/14.25 tff(l1_lattices_type, type, (
% 22.23/14.25 l1_lattices: $i > $o)).
% 22.23/14.25 tff(l2_lattices_type, type, (
% 22.23/14.25 l2_lattices: $i > $o)).
% 22.23/14.25 tff(v1_xboole_0_type, type, (
% 22.23/14.25 v1_xboole_0: $i > $o)).
% 22.23/14.25 tff(m1_filter_0_type, type, (
% 22.23/14.25 m1_filter_0: ( $i * $i ) > $o)).
% 22.23/14.25 tff(m1_filter_2_type, type, (
% 22.23/14.25 m1_filter_2: ( $i * $i ) > $o)).
% 22.23/14.25 tff(v9_lattices_type, type, (
% 22.23/14.25 v9_lattices: $i > $o)).
% 22.23/14.25 tff(v8_lattices_type, type, (
% 22.23/14.25 v8_lattices: $i > $o)).
% 22.23/14.25 tff(v7_lattices_type, type, (
% 22.23/14.25 v7_lattices: $i > $o)).
% 22.23/14.25 tff(v6_lattices_type, type, (
% 22.23/14.25 v6_lattices: $i > $o)).
% 22.23/14.25 tff(v5_lattices_type, type, (
% 22.23/14.25 v5_lattices: $i > $o)).
% 22.23/14.25 tff(v4_lattices_type, type, (
% 22.23/14.25 v4_lattices: $i > $o)).
% 22.23/14.25 tff(m2_lattice4_type, type, (
% 22.23/14.25 m2_lattice4: ( $i * $i ) > $o)).
% 22.23/14.25 tff(v13_lattices_type, type, (
% 22.23/14.25 v13_lattices: $i > $o)).
% 22.23/14.25 tff(k14_filter_2_type, type, (
% 22.23/14.25 k14_filter_2: ( $i * $i ) > $i)).
% 22.23/14.25 tff(k8_filter_2_type, type, (
% 22.23/14.25 k8_filter_2: ( $i * $i ) > $i)).
% 22.23/14.25 tff(1,plain,
% 22.23/14.25 (^[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)))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(2,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[1])).
% 22.23/14.25 tff(3,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(4,plain,
% 22.23/14.25 (^[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)))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(5,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[4])).
% 22.23/14.25 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 22.23/14.25 tff(7,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[6, 5])).
% 22.23/14.25 tff(8,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[7, 3])).
% 22.23/14.25 tff(9,plain,(
% 22.23/14.25 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 22.23/14.25 inference(skolemize,[status(sab)],[8])).
% 22.23/14.25 tff(10,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[9, 2])).
% 22.23/14.25 tff(11,plain,
% 22.23/14.25 (((m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))))) & v14_lattices(A!0) & ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))) <=> (m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))) & v14_lattices(A!0) & (~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(12,plain,
% 22.23/14.25 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(13,plain,
% 22.23/14.25 ((~(~v14_lattices(A!0))) <=> v14_lattices(A!0)),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(14,plain,
% 22.23/14.25 ((m2_filter_2(B!1, A!0) & ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(15,plain,
% 22.23/14.25 (((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))))) <=> ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(16,plain,
% 22.23/14.25 ((~(~m2_filter_2(B!1, A!0))) <=> m2_filter_2(B!1, A!0)),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(17,plain,
% 22.23/14.25 (((~(~m2_filter_2(B!1, A!0))) & ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m2_filter_2(B!1, A!0) & ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))))))),
% 22.23/14.25 inference(monotonicity,[status(thm)],[16, 15])).
% 22.23/14.25 tff(18,plain,
% 22.23/14.25 (((~(~m2_filter_2(B!1, A!0))) & ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))),
% 22.23/14.25 inference(transitivity,[status(thm)],[17, 14])).
% 22.23/14.25 tff(19,plain,
% 22.23/14.25 ((((~(~m2_filter_2(B!1, A!0))) & ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))) & (~(~v14_lattices(A!0))) & (~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))) <=> ((m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))))) & v14_lattices(A!0) & ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))),
% 22.23/14.25 inference(monotonicity,[status(thm)],[18, 13, 12])).
% 22.23/14.25 tff(20,plain,
% 22.23/14.25 ((((~(~m2_filter_2(B!1, A!0))) & ((~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))))) & (~(~v14_lattices(A!0))) & (~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))) <=> (m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))) & v14_lattices(A!0) & (~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 22.23/14.25 inference(transitivity,[status(thm)],[19, 11])).
% 22.23/14.25 tff(21,plain,
% 22.23/14.25 ((~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))) <=> (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(22,plain,
% 22.23/14.25 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) => ![B: $i] : (m2_filter_2(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m2_filter_2(C, A) => (~(r1_tarski(B, C) & r2_filter_2(A, C)))))))))) <=> (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(23,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) => ![B: $i] : (m2_filter_2(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m2_filter_2(C, A) => (~(r1_tarski(B, C) & r2_filter_2(A, C)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t34_filter_2')).
% 22.23/14.25 tff(24,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[23, 22])).
% 22.23/14.25 tff(25,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[24, 21])).
% 22.23/14.25 tff(26,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[25, 21])).
% 22.23/14.25 tff(27,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[26, 21])).
% 22.23/14.25 tff(28,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[27, 21])).
% 22.23/14.25 tff(29,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[28, 21])).
% 22.23/14.25 tff(30,plain,
% 22.23/14.25 (~![A: $i] : (![B: $i] : ((~m2_filter_2(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r1_tarski(B, C) & r2_filter_2(A, C))))))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[29, 21])).
% 22.23/14.25 tff(31,plain,
% 22.23/14.25 (m2_filter_2(B!1, A!0) & (~(B!1 = u1_struct_0(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))) & v14_lattices(A!0) & (~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[30, 20])).
% 22.23/14.25 tff(32,plain,
% 22.23/14.25 (l3_lattices(A!0)),
% 22.23/14.25 inference(and_elim,[status(thm)],[31])).
% 22.23/14.25 tff(33,plain,
% 22.23/14.25 (((~![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))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(34,plain,
% 22.23/14.25 ((~![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))))),
% 22.23/14.25 inference(quant_inst,[status(thm)],[])).
% 22.23/14.25 tff(35,plain,
% 22.23/14.25 ((~![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)))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[34, 33])).
% 22.23/14.25 tff(36,plain,
% 22.23/14.25 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[35, 32, 10])).
% 22.23/14.25 tff(37,plain,
% 22.23/14.25 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 22.23/14.25 inference(symmetry,[status(thm)],[36])).
% 22.23/14.25 tff(38,plain,
% 22.23/14.25 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(k1_lattice2(A!0))),
% 22.23/14.25 inference(monotonicity,[status(thm)],[37])).
% 22.23/14.25 tff(39,plain,
% 22.23/14.25 (k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 22.23/14.25 inference(monotonicity,[status(thm)],[38])).
% 22.23/14.25 tff(40,plain,
% 22.23/14.25 (k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.25 inference(symmetry,[status(thm)],[39])).
% 22.23/14.25 tff(41,plain,
% 22.23/14.25 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.25 inference(symmetry,[status(thm)],[38])).
% 22.23/14.25 tff(42,plain,
% 22.23/14.25 (g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.25 inference(monotonicity,[status(thm)],[41])).
% 22.23/14.25 tff(43,plain,
% 22.23/14.25 (g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.25 inference(symmetry,[status(thm)],[42])).
% 22.23/14.25 tff(44,plain,
% 22.23/14.25 (^[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)))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(45,plain,
% 22.23/14.25 (![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))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[44])).
% 22.23/14.25 tff(46,plain,
% 22.23/14.25 (![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))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(47,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 22.23/14.25 tff(48,plain,
% 22.23/14.25 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[47, 46])).
% 22.23/14.25 tff(49,plain,(
% 22.23/14.25 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 22.23/14.25 inference(skolemize,[status(sab)],[48])).
% 22.23/14.25 tff(50,plain,
% 22.23/14.25 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[49, 45])).
% 22.23/14.25 tff(51,plain,
% 22.23/14.25 ((~![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)))),
% 22.23/14.25 inference(quant_inst,[status(thm)],[])).
% 22.23/14.25 tff(52,plain,
% 22.23/14.25 (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))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[51, 50])).
% 22.23/14.25 tff(53,plain,
% 22.23/14.25 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(54,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[53])).
% 22.23/14.25 tff(55,plain,
% 22.23/14.25 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(56,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[55])).
% 22.23/14.25 tff(57,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(58,plain,
% 22.23/14.25 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(59,plain,
% 22.23/14.25 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[58])).
% 22.23/14.25 tff(60,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 22.23/14.25 tff(61,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[60, 59])).
% 22.23/14.25 tff(62,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[61, 57])).
% 22.23/14.25 tff(63,plain,(
% 22.23/14.25 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 22.23/14.25 inference(skolemize,[status(sab)],[62])).
% 22.23/14.25 tff(64,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[63, 56])).
% 22.23/14.25 tff(65,plain,
% 22.23/14.25 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[64, 54])).
% 22.23/14.25 tff(66,plain,
% 22.23/14.25 (((~![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)))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(67,plain,
% 22.23/14.25 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 22.23/14.25 inference(quant_inst,[status(thm)],[])).
% 22.23/14.25 tff(68,plain,
% 22.23/14.25 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[67, 66])).
% 22.23/14.25 tff(69,plain,
% 22.23/14.25 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[68, 32, 65])).
% 22.23/14.25 tff(70,plain,
% 22.23/14.25 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 22.23/14.25 inference(tautology,[status(thm)],[])).
% 22.23/14.25 tff(71,plain,
% 22.23/14.25 (l1_lattices(A!0)),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[70, 69])).
% 22.23/14.25 tff(72,plain,
% 22.23/14.25 (^[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)))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(73,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[72])).
% 22.23/14.25 tff(74,plain,
% 22.23/14.25 (^[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)))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(75,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[74])).
% 22.23/14.25 tff(76,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(77,plain,
% 22.23/14.25 (^[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))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(78,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[77])).
% 22.23/14.25 tff(79,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 22.23/14.25 tff(80,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[79, 78])).
% 22.23/14.25 tff(81,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[80, 76])).
% 22.23/14.25 tff(82,plain,(
% 22.23/14.25 ![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))))),
% 22.23/14.25 inference(skolemize,[status(sab)],[81])).
% 22.23/14.25 tff(83,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[82, 75])).
% 22.23/14.25 tff(84,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[83, 73])).
% 22.23/14.25 tff(85,plain,
% 22.23/14.25 (((~![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))))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(86,plain,
% 22.23/14.25 ((~![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))))))),
% 22.23/14.25 inference(quant_inst,[status(thm)],[])).
% 22.23/14.25 tff(87,plain,
% 22.23/14.25 ((~![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)))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[86, 85])).
% 22.23/14.25 tff(88,plain,
% 22.23/14.25 ((~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)))))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[87, 84])).
% 22.23/14.25 tff(89,plain,
% 22.23/14.25 (~((~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))))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[88, 71])).
% 22.23/14.25 tff(90,plain,
% 22.23/14.25 (((~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))),
% 22.23/14.25 inference(tautology,[status(thm)],[])).
% 22.23/14.25 tff(91,plain,
% 22.23/14.25 (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))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[90, 89])).
% 22.23/14.25 tff(92,plain,
% 22.23/14.25 ((~(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))),
% 22.23/14.25 inference(tautology,[status(thm)],[])).
% 22.23/14.25 tff(93,plain,
% 22.23/14.25 ((~(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))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[92, 91])).
% 22.23/14.25 tff(94,plain,
% 22.23/14.25 (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))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[93, 52])).
% 22.23/14.25 tff(95,plain,
% 22.23/14.25 ((~![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)))),
% 22.23/14.25 inference(quant_inst,[status(thm)],[])).
% 22.23/14.25 tff(96,plain,
% 22.23/14.25 (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))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[95, 50])).
% 22.23/14.25 tff(97,plain,
% 22.23/14.25 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 22.23/14.25 inference(tautology,[status(thm)],[])).
% 22.23/14.25 tff(98,plain,
% 22.23/14.25 (l2_lattices(A!0)),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[97, 69])).
% 22.23/14.25 tff(99,plain,
% 22.23/14.25 (^[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)))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(100,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[99])).
% 22.23/14.25 tff(101,plain,
% 22.23/14.25 (^[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)))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(102,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[101])).
% 22.23/14.25 tff(103,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(104,plain,
% 22.23/14.25 (^[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))))))),
% 22.23/14.25 inference(bind,[status(th)],[])).
% 22.23/14.25 tff(105,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(quant_intro,[status(thm)],[104])).
% 22.23/14.25 tff(106,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 22.23/14.25 tff(107,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[106, 105])).
% 22.23/14.25 tff(108,plain,
% 22.23/14.25 (![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))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[107, 103])).
% 22.23/14.25 tff(109,plain,(
% 22.23/14.25 ![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))))),
% 22.23/14.25 inference(skolemize,[status(sab)],[108])).
% 22.23/14.25 tff(110,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[109, 102])).
% 22.23/14.25 tff(111,plain,
% 22.23/14.25 (![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))))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[110, 100])).
% 22.23/14.25 tff(112,plain,
% 22.23/14.25 (((~![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))))))),
% 22.23/14.25 inference(rewrite,[status(thm)],[])).
% 22.23/14.25 tff(113,plain,
% 22.23/14.25 ((~![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))))))),
% 22.23/14.25 inference(quant_inst,[status(thm)],[])).
% 22.23/14.25 tff(114,plain,
% 22.23/14.25 ((~![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)))))),
% 22.23/14.25 inference(modus_ponens,[status(thm)],[113, 112])).
% 22.23/14.25 tff(115,plain,
% 22.23/14.25 ((~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)))))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[114, 111])).
% 22.23/14.25 tff(116,plain,
% 22.23/14.25 (~((~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))))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[115, 98])).
% 22.23/14.25 tff(117,plain,
% 22.23/14.25 (((~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))),
% 22.23/14.25 inference(tautology,[status(thm)],[])).
% 22.23/14.25 tff(118,plain,
% 22.23/14.25 (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))),
% 22.23/14.25 inference(unit_resolution,[status(thm)],[117, 116])).
% 22.23/14.25 tff(119,plain,
% 22.23/14.25 ((~(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))),
% 22.23/14.25 inference(tautology,[status(thm)],[])).
% 22.23/14.25 tff(120,plain,
% 22.23/14.25 ((~(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))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[119, 118])).
% 22.23/14.26 tff(121,plain,
% 22.23/14.26 (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))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[120, 96])).
% 22.23/14.26 tff(122,plain,
% 22.23/14.26 (((~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))),
% 22.23/14.26 inference(tautology,[status(thm)],[])).
% 22.23/14.26 tff(123,plain,
% 22.23/14.26 (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))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[122, 116])).
% 22.23/14.26 tff(124,plain,
% 22.23/14.26 (((~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))),
% 22.23/14.26 inference(tautology,[status(thm)],[])).
% 22.23/14.26 tff(125,plain,
% 22.23/14.26 (v1_funct_1(u2_lattices(A!0))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[124, 116])).
% 22.23/14.26 tff(126,plain,
% 22.23/14.26 (((~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))),
% 22.23/14.26 inference(tautology,[status(thm)],[])).
% 22.23/14.26 tff(127,plain,
% 22.23/14.26 (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))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[126, 89])).
% 22.23/14.26 tff(128,plain,
% 22.23/14.26 (((~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))),
% 22.23/14.26 inference(tautology,[status(thm)],[])).
% 22.23/14.26 tff(129,plain,
% 22.23/14.26 (v1_funct_1(u1_lattices(A!0))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[128, 89])).
% 22.23/14.26 tff(130,plain,
% 22.23/14.26 (^[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)))))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(131,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[130])).
% 22.23/14.26 tff(132,plain,
% 22.23/14.26 (^[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))))))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(133,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[132])).
% 22.23/14.26 tff(134,plain,
% 22.23/14.26 (![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))))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(135,plain,
% 22.23/14.26 (^[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))))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(136,plain,
% 22.23/14.26 (![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))))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[135])).
% 22.23/14.26 tff(137,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 22.23/14.26 tff(138,plain,
% 22.23/14.26 (![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))))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[137, 136])).
% 22.23/14.26 tff(139,plain,
% 22.23/14.26 (![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))))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[138, 134])).
% 22.23/14.26 tff(140,plain,(
% 22.23/14.26 ![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))))),
% 22.23/14.26 inference(skolemize,[status(sab)],[139])).
% 22.23/14.26 tff(141,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[140, 133])).
% 22.23/14.26 tff(142,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[141, 131])).
% 22.23/14.26 tff(143,plain,
% 22.23/14.26 (((~![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(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))) | (~((~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(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))) | (~((~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)))))))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(144,plain,
% 22.23/14.26 (((~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(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))) | (~((~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)))))))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(145,plain,
% 22.23/14.26 ((~((~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))))))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(146,plain,
% 22.23/14.26 (((~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)))))))),
% 22.23/14.26 inference(monotonicity,[status(thm)],[145])).
% 22.23/14.26 tff(147,plain,
% 22.23/14.26 (((~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(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))) | (~((~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)))))))),
% 22.23/14.26 inference(transitivity,[status(thm)],[146, 144])).
% 22.23/14.26 tff(148,plain,
% 22.23/14.26 (((~![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(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))) | (~((~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))))))))),
% 22.23/14.26 inference(monotonicity,[status(thm)],[147])).
% 22.23/14.26 tff(149,plain,
% 22.23/14.26 (((~![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(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))) | (~((~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)))))))),
% 22.23/14.26 inference(transitivity,[status(thm)],[148, 143])).
% 22.23/14.26 tff(150,plain,
% 22.23/14.26 ((~![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)))))))),
% 22.23/14.26 inference(quant_inst,[status(thm)],[])).
% 22.23/14.26 tff(151,plain,
% 22.23/14.26 ((~![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(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))) | (~((~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))))))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[150, 149])).
% 22.23/14.26 tff(152,plain,
% 22.23/14.26 ((~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(u1_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))))))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[151, 142, 129, 127, 125, 123])).
% 22.23/14.26 tff(153,plain,
% 22.23/14.26 (~((~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)))))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[152, 121, 94])).
% 22.23/14.26 tff(154,plain,
% 22.23/14.26 (((~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)))),
% 22.23/14.26 inference(tautology,[status(thm)],[])).
% 22.23/14.26 tff(155,plain,
% 22.23/14.26 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[154, 153])).
% 22.23/14.26 tff(156,plain,
% 22.23/14.26 (((~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)))),
% 22.23/14.26 inference(tautology,[status(thm)],[])).
% 22.23/14.26 tff(157,plain,
% 22.23/14.26 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[156, 153])).
% 22.23/14.26 tff(158,plain,
% 22.23/14.26 (^[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))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(159,plain,
% 22.23/14.26 (![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)))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[158])).
% 22.23/14.26 tff(160,plain,
% 22.23/14.26 (![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)))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(161,plain,
% 22.23/14.26 (^[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)))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(162,plain,
% 22.23/14.26 (![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)))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[161])).
% 22.23/14.26 tff(163,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 22.23/14.26 tff(164,plain,
% 22.23/14.26 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[163, 162])).
% 22.23/14.26 tff(165,plain,
% 22.23/14.26 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[164, 160])).
% 22.23/14.26 tff(166,plain,(
% 22.23/14.26 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.26 inference(skolemize,[status(sab)],[165])).
% 22.23/14.26 tff(167,plain,
% 22.23/14.26 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[166, 159])).
% 22.23/14.26 tff(168,plain,
% 22.23/14.26 (((~![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))))))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(169,plain,
% 22.23/14.26 (((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))))))),
% 22.23/14.26 inference(rewrite,[status(thm)],[])).
% 22.23/14.26 tff(170,plain,
% 22.23/14.26 (((~![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)))))))),
% 22.23/14.26 inference(monotonicity,[status(thm)],[169])).
% 22.23/14.26 tff(171,plain,
% 22.23/14.26 (((~![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))))))),
% 22.23/14.26 inference(transitivity,[status(thm)],[170, 168])).
% 22.23/14.26 tff(172,plain,
% 22.23/14.26 ((~![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)))))),
% 22.23/14.26 inference(quant_inst,[status(thm)],[])).
% 22.23/14.26 tff(173,plain,
% 22.23/14.26 ((~![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)))))),
% 22.23/14.26 inference(modus_ponens,[status(thm)],[172, 171])).
% 22.23/14.26 tff(174,plain,
% 22.23/14.26 ((~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)))))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[173, 167])).
% 22.23/14.26 tff(175,plain,
% 22.23/14.26 (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))))),
% 22.23/14.26 inference(unit_resolution,[status(thm)],[174, 157, 155])).
% 22.23/14.26 tff(176,plain,
% 22.23/14.26 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.26 inference(transitivity,[status(thm)],[175, 43])).
% 22.23/14.26 tff(177,plain,
% 22.23/14.26 (^[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)))))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(178,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[177])).
% 22.23/14.26 tff(179,plain,
% 22.23/14.26 (^[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)))))))),
% 22.23/14.26 inference(bind,[status(th)],[])).
% 22.23/14.26 tff(180,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(quant_intro,[status(thm)],[179])).
% 22.23/14.26 tff(181,plain,
% 22.23/14.26 (![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))))))),
% 22.23/14.26 inference(transitivity,[status(thm)],[180, 178])).
% 22.23/14.26 tff(182,plain,
% 22.23/14.26 (^[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))))))))),
% 22.23/14.27 inference(bind,[status(th)],[])).
% 22.23/14.27 tff(183,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(quant_intro,[status(thm)],[182])).
% 22.23/14.27 tff(184,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(rewrite,[status(thm)],[])).
% 22.23/14.27 tff(185,plain,
% 22.23/14.27 (^[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))))))),
% 22.23/14.27 inference(bind,[status(th)],[])).
% 22.23/14.27 tff(186,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(quant_intro,[status(thm)],[185])).
% 22.23/14.27 tff(187,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g3_lattices')).
% 22.23/14.27 tff(188,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[187, 186])).
% 22.23/14.27 tff(189,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[188, 184])).
% 22.23/14.27 tff(190,plain,(
% 22.23/14.27 ![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))))),
% 22.23/14.27 inference(skolemize,[status(sab)],[189])).
% 22.23/14.27 tff(191,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[190, 183])).
% 22.23/14.27 tff(192,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[191, 181])).
% 22.23/14.27 tff(193,plain,
% 22.23/14.27 (((~![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(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))) | ![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(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))) | ![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))))))),
% 22.23/14.27 inference(rewrite,[status(thm)],[])).
% 22.23/14.27 tff(194,plain,
% 22.23/14.27 (((~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(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))) | ![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))))))),
% 22.23/14.27 inference(rewrite,[status(thm)],[])).
% 22.23/14.27 tff(195,plain,
% 22.23/14.27 (((~![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(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))) | ![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)))))))),
% 22.23/14.27 inference(monotonicity,[status(thm)],[194])).
% 22.23/14.27 tff(196,plain,
% 22.23/14.27 (((~![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(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))) | ![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))))))),
% 22.23/14.27 inference(transitivity,[status(thm)],[195, 193])).
% 22.23/14.27 tff(197,plain,
% 22.23/14.27 ((~![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))))))),
% 22.23/14.27 inference(quant_inst,[status(thm)],[])).
% 22.23/14.27 tff(198,plain,
% 22.23/14.27 ((~![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(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))) | ![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)))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[197, 196])).
% 22.23/14.27 tff(199,plain,
% 22.23/14.27 ((~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(u1_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)))))),
% 22.23/14.27 inference(unit_resolution,[status(thm)],[198, 192, 129, 127, 125, 123])).
% 22.23/14.27 tff(200,plain,
% 22.23/14.27 (![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)))))),
% 22.23/14.27 inference(unit_resolution,[status(thm)],[199, 121, 94])).
% 22.23/14.27 tff(201,plain,
% 22.23/14.27 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.27 inference(rewrite,[status(thm)],[])).
% 22.23/14.27 tff(202,plain,
% 22.23/14.27 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.27 inference(quant_inst,[status(thm)],[])).
% 22.23/14.27 tff(203,plain,
% 22.23/14.27 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[202, 201])).
% 22.23/14.27 tff(204,plain,
% 22.23/14.27 ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.27 inference(unit_resolution,[status(thm)],[203, 200])).
% 22.23/14.27 tff(205,plain,
% 22.23/14.27 (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.23/14.27 inference(unit_resolution,[status(thm)],[204, 176])).
% 22.23/14.27 tff(206,plain,
% 22.23/14.27 (((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))),
% 22.23/14.27 inference(tautology,[status(thm)],[])).
% 22.23/14.27 tff(207,plain,
% 22.23/14.27 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 22.23/14.27 inference(unit_resolution,[status(thm)],[206, 205])).
% 22.23/14.27 tff(208,plain,
% 22.23/14.27 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 22.23/14.27 inference(monotonicity,[status(thm)],[207])).
% 22.23/14.27 tff(209,plain,
% 22.23/14.27 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.27 inference(transitivity,[status(thm)],[208, 40])).
% 22.23/14.27 tff(210,plain,
% 22.23/14.27 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.23/14.27 inference(monotonicity,[status(thm)],[209])).
% 22.23/14.27 tff(211,plain,
% 22.23/14.27 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 22.23/14.27 inference(symmetry,[status(thm)],[210])).
% 22.23/14.27 tff(212,plain,
% 22.23/14.27 (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))),
% 22.23/14.27 inference(monotonicity,[status(thm)],[37])).
% 22.23/14.27 tff(213,plain,
% 22.23/14.27 (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)))),
% 22.23/14.27 inference(symmetry,[status(thm)],[212])).
% 22.23/14.27 tff(214,plain,
% 22.23/14.27 ((~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))))),
% 22.23/14.27 inference(monotonicity,[status(thm)],[213])).
% 22.23/14.27 tff(215,plain,
% 22.23/14.27 (^[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)))))))),
% 22.23/14.27 inference(bind,[status(th)],[])).
% 22.23/14.27 tff(216,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(quant_intro,[status(thm)],[215])).
% 22.23/14.27 tff(217,plain,
% 22.23/14.27 (^[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))))))))),
% 22.23/14.27 inference(bind,[status(th)],[])).
% 22.23/14.27 tff(218,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(quant_intro,[status(thm)],[217])).
% 22.23/14.27 tff(219,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(rewrite,[status(thm)],[])).
% 22.23/14.27 tff(220,plain,
% 22.23/14.27 (^[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))))))),
% 22.23/14.27 inference(bind,[status(th)],[])).
% 22.23/14.27 tff(221,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(quant_intro,[status(thm)],[220])).
% 22.23/14.27 tff(222,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 22.23/14.27 tff(223,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[222, 221])).
% 22.23/14.27 tff(224,plain,
% 22.23/14.27 (![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))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[223, 219])).
% 22.23/14.27 tff(225,plain,(
% 22.23/14.27 ![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))))),
% 22.23/14.27 inference(skolemize,[status(sab)],[224])).
% 22.23/14.27 tff(226,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[225, 218])).
% 22.23/14.27 tff(227,plain,
% 22.23/14.27 (![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))))))),
% 22.23/14.27 inference(modus_ponens,[status(thm)],[226, 216])).
% 22.23/14.27 tff(228,plain,
% 22.23/14.27 (v10_lattices(A!0)),
% 22.23/14.27 inference(and_elim,[status(thm)],[31])).
% 22.23/14.27 tff(229,plain,
% 22.23/14.27 (~v3_struct_0(A!0)),
% 22.23/14.27 inference(and_elim,[status(thm)],[31])).
% 22.23/14.27 tff(230,plain,
% 22.23/14.27 (((~![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))))))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(231,plain,
% 22.23/14.28 ((~![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))))))),
% 22.23/14.28 inference(quant_inst,[status(thm)],[])).
% 22.23/14.28 tff(232,plain,
% 22.23/14.28 ((~![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)))))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[231, 230])).
% 22.23/14.28 tff(233,plain,
% 22.23/14.28 (~(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))))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[232, 229, 228, 32, 227])).
% 22.23/14.28 tff(234,plain,
% 22.23/14.28 ((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)))),
% 22.23/14.28 inference(tautology,[status(thm)],[])).
% 22.23/14.28 tff(235,plain,
% 22.23/14.28 (~v3_struct_0(k1_lattice2(A!0))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[234, 233])).
% 22.23/14.28 tff(236,plain,
% 22.23/14.28 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[235, 214])).
% 22.23/14.28 tff(237,plain,
% 22.23/14.28 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 22.23/14.28 inference(monotonicity,[status(thm)],[37])).
% 22.23/14.28 tff(238,plain,
% 22.23/14.28 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(symmetry,[status(thm)],[237])).
% 22.23/14.28 tff(239,plain,
% 22.23/14.28 ((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))),
% 22.23/14.28 inference(tautology,[status(thm)],[])).
% 22.23/14.28 tff(240,plain,
% 22.23/14.28 (v10_lattices(k1_lattice2(A!0))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[239, 233])).
% 22.23/14.28 tff(241,plain,
% 22.23/14.28 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[240, 238])).
% 22.23/14.28 tff(242,plain,
% 22.23/14.28 (^[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))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(243,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[242])).
% 22.23/14.28 tff(244,plain,
% 22.23/14.28 (^[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))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(245,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[244])).
% 22.23/14.28 tff(246,plain,
% 22.23/14.28 (^[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))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(247,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[246])).
% 22.23/14.28 tff(248,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(transitivity,[status(thm)],[247, 245])).
% 22.23/14.28 tff(249,plain,
% 22.23/14.28 (^[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)))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(250,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[249])).
% 22.23/14.28 tff(251,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(252,plain,
% 22.23/14.28 (^[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)))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(253,plain,
% 22.23/14.28 (![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)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[252])).
% 22.23/14.28 tff(254,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/sandbox2/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 22.23/14.28 tff(255,plain,
% 22.23/14.28 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[254, 253])).
% 22.23/14.28 tff(256,plain,
% 22.23/14.28 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[255, 251])).
% 22.23/14.28 tff(257,plain,(
% 22.23/14.28 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 22.23/14.28 inference(skolemize,[status(sab)],[256])).
% 22.23/14.28 tff(258,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[257, 250])).
% 22.23/14.28 tff(259,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[258, 248])).
% 22.23/14.28 tff(260,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[259, 243])).
% 22.23/14.28 tff(261,plain,
% 22.23/14.28 (((~![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)))))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(262,plain,
% 22.23/14.28 ((~![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)))))),
% 22.23/14.28 inference(quant_inst,[status(thm)],[])).
% 22.23/14.28 tff(263,plain,
% 22.23/14.28 ((~![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))))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[262, 261])).
% 22.23/14.28 tff(264,plain,
% 22.23/14.28 (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))))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[263, 260])).
% 22.23/14.28 tff(265,plain,
% 22.23/14.28 (![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))))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[264, 241, 157, 236])).
% 22.23/14.28 tff(266,plain,
% 22.23/14.28 ((~![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(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.28 inference(quant_inst,[status(thm)],[])).
% 22.23/14.28 tff(267,plain,
% 22.23/14.28 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[266, 265])).
% 22.23/14.28 tff(268,plain,
% 22.23/14.28 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(269,plain,
% 22.23/14.28 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[268])).
% 22.23/14.28 tff(270,plain,
% 22.23/14.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(271,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[270])).
% 22.23/14.28 tff(272,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(273,plain,
% 22.23/14.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(274,plain,
% 22.23/14.28 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[273])).
% 22.23/14.28 tff(275,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 22.23/14.28 tff(276,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[275, 274])).
% 22.23/14.28 tff(277,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[276, 272])).
% 22.23/14.28 tff(278,plain,(
% 22.23/14.28 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 22.23/14.28 inference(skolemize,[status(sab)],[277])).
% 22.23/14.28 tff(279,plain,
% 22.23/14.28 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[278, 271])).
% 22.23/14.28 tff(280,plain,
% 22.23/14.28 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[279, 269])).
% 22.23/14.28 tff(281,plain,
% 22.23/14.28 (m2_filter_2(B!1, A!0)),
% 22.23/14.28 inference(and_elim,[status(thm)],[31])).
% 22.23/14.28 tff(282,plain,
% 22.23/14.28 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(283,plain,
% 22.23/14.28 ((v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(284,plain,
% 22.23/14.28 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))))),
% 22.23/14.28 inference(monotonicity,[status(thm)],[283])).
% 22.23/14.28 tff(285,plain,
% 22.23/14.28 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 22.23/14.28 inference(transitivity,[status(thm)],[284, 282])).
% 22.23/14.28 tff(286,plain,
% 22.23/14.28 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 22.23/14.28 inference(quant_inst,[status(thm)],[])).
% 22.23/14.28 tff(287,plain,
% 22.23/14.28 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[286, 285])).
% 22.23/14.28 tff(288,plain,
% 22.23/14.28 (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[287, 281, 229, 228, 32, 280])).
% 22.23/14.28 tff(289,plain,
% 22.23/14.28 (k7_filter_2(A!0, B!1) = k15_filter_2(A!0, B!1)),
% 22.23/14.28 inference(symmetry,[status(thm)],[288])).
% 22.23/14.28 tff(290,plain,
% 22.23/14.28 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 22.23/14.28 inference(monotonicity,[status(thm)],[289, 37])).
% 22.23/14.28 tff(291,plain,
% 22.23/14.28 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) <=> m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(symmetry,[status(thm)],[290])).
% 22.23/14.28 tff(292,plain,
% 22.23/14.28 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(293,plain,
% 22.23/14.28 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[292])).
% 22.23/14.28 tff(294,plain,
% 22.23/14.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(295,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[294])).
% 22.23/14.28 tff(296,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(297,plain,
% 22.23/14.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(298,plain,
% 22.23/14.28 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[297])).
% 22.23/14.28 tff(299,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k15_filter_2')).
% 22.23/14.28 tff(300,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[299, 298])).
% 22.23/14.28 tff(301,plain,
% 22.23/14.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[300, 296])).
% 22.23/14.28 tff(302,plain,(
% 22.23/14.28 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 22.23/14.28 inference(skolemize,[status(sab)],[301])).
% 22.23/14.28 tff(303,plain,
% 22.23/14.28 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[302, 295])).
% 22.23/14.28 tff(304,plain,
% 22.23/14.28 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[303, 293])).
% 22.23/14.28 tff(305,plain,
% 22.23/14.28 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(306,plain,
% 22.23/14.28 ((v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(307,plain,
% 22.23/14.28 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 22.23/14.28 inference(monotonicity,[status(thm)],[306])).
% 22.23/14.28 tff(308,plain,
% 22.23/14.28 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 22.23/14.28 inference(transitivity,[status(thm)],[307, 305])).
% 22.23/14.28 tff(309,plain,
% 22.23/14.28 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 22.23/14.28 inference(quant_inst,[status(thm)],[])).
% 22.23/14.28 tff(310,plain,
% 22.23/14.28 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[309, 308])).
% 22.23/14.28 tff(311,plain,
% 22.23/14.28 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[310, 281, 229, 228, 32, 304])).
% 22.23/14.28 tff(312,plain,
% 22.23/14.28 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[311, 291])).
% 22.23/14.28 tff(313,plain,
% 22.23/14.28 ((~(m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(tautology,[status(thm)],[])).
% 22.23/14.28 tff(314,plain,
% 22.23/14.28 (m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.28 inference(unit_resolution,[status(thm)],[313, 312, 267])).
% 22.23/14.28 tff(315,plain,
% 22.23/14.28 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(A!0)),
% 22.23/14.28 inference(symmetry,[status(thm)],[207])).
% 22.23/14.28 tff(316,plain,
% 22.23/14.28 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 22.23/14.28 inference(transitivity,[status(thm)],[38, 315])).
% 22.23/14.28 tff(317,plain,
% 22.23/14.28 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(318,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[317])).
% 22.23/14.28 tff(319,plain,
% 22.23/14.28 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(320,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[319])).
% 22.23/14.28 tff(321,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 22.23/14.28 inference(transitivity,[status(thm)],[320, 318])).
% 22.23/14.28 tff(322,plain,
% 22.23/14.28 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(323,plain,
% 22.23/14.28 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[322])).
% 22.23/14.28 tff(324,plain,
% 22.23/14.28 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(325,plain,
% 22.23/14.28 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 22.23/14.28 inference(bind,[status(th)],[])).
% 22.23/14.28 tff(326,plain,
% 22.23/14.28 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 22.23/14.28 inference(quant_intro,[status(thm)],[325])).
% 22.23/14.28 tff(327,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 22.23/14.28 tff(328,plain,
% 22.23/14.28 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[327, 326])).
% 22.23/14.28 tff(329,plain,
% 22.23/14.28 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[328, 324])).
% 22.23/14.28 tff(330,plain,(
% 22.23/14.28 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 22.23/14.28 inference(skolemize,[status(sab)],[329])).
% 22.23/14.28 tff(331,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[330, 323])).
% 22.23/14.28 tff(332,plain,
% 22.23/14.28 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 22.23/14.28 inference(modus_ponens,[status(thm)],[331, 321])).
% 22.23/14.28 tff(333,plain,
% 22.23/14.28 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 22.23/14.28 inference(rewrite,[status(thm)],[])).
% 22.23/14.28 tff(334,plain,
% 22.23/14.28 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(335,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[334, 333])).
% 22.23/14.29 tff(336,plain,
% 22.23/14.29 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[335, 229, 228, 32, 332])).
% 22.23/14.29 tff(337,plain,
% 22.23/14.29 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(338,plain,
% 22.23/14.29 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(339,plain,
% 22.23/14.29 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[338, 337])).
% 22.23/14.29 tff(340,plain,
% 22.23/14.29 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[339, 281, 336])).
% 22.23/14.29 tff(341,plain,
% 22.23/14.29 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 22.23/14.29 inference(tautology,[status(thm)],[])).
% 22.23/14.29 tff(342,plain,
% 22.23/14.29 (m2_lattice4(B!1, A!0)),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[341, 340])).
% 22.23/14.29 tff(343,plain,
% 22.23/14.29 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(344,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[343])).
% 22.23/14.29 tff(345,plain,
% 22.23/14.29 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(346,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[345])).
% 22.23/14.29 tff(347,plain,
% 22.23/14.29 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(348,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[347])).
% 22.23/14.29 tff(349,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 22.23/14.29 inference(transitivity,[status(thm)],[348, 346])).
% 22.23/14.29 tff(350,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(351,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[350])).
% 22.23/14.29 tff(352,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(353,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(354,plain,
% 22.23/14.29 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[353])).
% 22.23/14.29 tff(355,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 22.23/14.29 tff(356,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[355, 354])).
% 22.23/14.29 tff(357,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[356, 352])).
% 22.23/14.29 tff(358,plain,(
% 22.23/14.29 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(skolemize,[status(sab)],[357])).
% 22.23/14.29 tff(359,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[358, 351])).
% 22.23/14.29 tff(360,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[359, 349])).
% 22.23/14.29 tff(361,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[360, 344])).
% 22.23/14.29 tff(362,plain,
% 22.23/14.29 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(363,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(364,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[363, 362])).
% 22.23/14.29 tff(365,plain,
% 22.23/14.29 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[364, 229, 228, 32, 361])).
% 22.23/14.29 tff(366,plain,
% 22.23/14.29 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(367,plain,
% 22.23/14.29 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(368,plain,
% 22.23/14.29 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[367, 366])).
% 22.23/14.29 tff(369,plain,
% 22.23/14.29 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[368, 365, 342])).
% 22.23/14.29 tff(370,plain,
% 22.23/14.29 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(371,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[370])).
% 22.23/14.29 tff(372,plain,
% 22.23/14.29 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(373,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[372])).
% 22.23/14.29 tff(374,plain,
% 22.23/14.29 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(375,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[374])).
% 22.23/14.29 tff(376,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(transitivity,[status(thm)],[375, 373])).
% 22.23/14.29 tff(377,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(378,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[377])).
% 22.23/14.29 tff(379,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(380,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(381,plain,
% 22.23/14.29 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[380])).
% 22.23/14.29 tff(382,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_filter_2')).
% 22.23/14.29 tff(383,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[382, 381])).
% 22.23/14.29 tff(384,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[383, 379])).
% 22.23/14.29 tff(385,plain,(
% 22.23/14.29 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(skolemize,[status(sab)],[384])).
% 22.23/14.29 tff(386,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[385, 378])).
% 22.23/14.29 tff(387,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[386, 376])).
% 22.23/14.29 tff(388,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[387, 371])).
% 22.23/14.29 tff(389,plain,
% 22.23/14.29 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(390,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(391,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[390, 389])).
% 22.23/14.29 tff(392,plain,
% 22.23/14.29 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[391, 229, 228, 32, 388])).
% 22.23/14.29 tff(393,plain,
% 22.23/14.29 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(394,plain,
% 22.23/14.29 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(395,plain,
% 22.23/14.29 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[394, 393])).
% 22.23/14.29 tff(396,plain,
% 22.23/14.29 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[395, 392])).
% 22.23/14.29 tff(397,plain,
% 22.23/14.29 (k7_filter_2(A!0, B!1) = B!1),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[396, 369])).
% 22.23/14.29 tff(398,plain,
% 22.23/14.29 ((k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> (B!1 = u1_struct_0(A!0))),
% 22.23/14.29 inference(monotonicity,[status(thm)],[397, 316])).
% 22.23/14.29 tff(399,plain,
% 22.23/14.29 ((B!1 = u1_struct_0(A!0)) <=> (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.29 inference(symmetry,[status(thm)],[398])).
% 22.23/14.29 tff(400,plain,
% 22.23/14.29 ((~(B!1 = u1_struct_0(A!0))) <=> (~(k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.23/14.29 inference(monotonicity,[status(thm)],[399])).
% 22.23/14.29 tff(401,plain,
% 22.23/14.29 (~(B!1 = u1_struct_0(A!0))),
% 22.23/14.29 inference(and_elim,[status(thm)],[31])).
% 22.23/14.29 tff(402,plain,
% 22.23/14.29 (~(k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[401, 400])).
% 22.23/14.29 tff(403,plain,
% 22.23/14.29 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v13_lattices(k1_lattice2(A!0))),
% 22.23/14.29 inference(monotonicity,[status(thm)],[37])).
% 22.23/14.29 tff(404,plain,
% 22.23/14.29 (v13_lattices(k1_lattice2(A!0)) <=> v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.29 inference(symmetry,[status(thm)],[403])).
% 22.23/14.29 tff(405,plain,
% 22.23/14.29 (^[A: $i] : refl((v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(406,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[405])).
% 22.23/14.29 tff(407,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(408,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[407])).
% 22.23/14.29 tff(409,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(410,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(411,plain,
% 22.23/14.29 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[410])).
% 22.23/14.29 tff(412,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t64_lattice2')).
% 22.23/14.29 tff(413,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[412, 411])).
% 22.23/14.29 tff(414,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[413, 409])).
% 22.23/14.29 tff(415,plain,(
% 22.23/14.29 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 22.23/14.29 inference(skolemize,[status(sab)],[414])).
% 22.23/14.29 tff(416,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[415, 408])).
% 22.23/14.29 tff(417,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[416, 406])).
% 22.23/14.29 tff(418,plain,
% 22.23/14.29 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(419,plain,
% 22.23/14.29 ((v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(420,plain,
% 22.23/14.29 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))))),
% 22.23/14.29 inference(monotonicity,[status(thm)],[419])).
% 22.23/14.29 tff(421,plain,
% 22.23/14.29 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 22.23/14.29 inference(transitivity,[status(thm)],[420, 418])).
% 22.23/14.29 tff(422,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 22.23/14.29 inference(quant_inst,[status(thm)],[])).
% 22.23/14.29 tff(423,plain,
% 22.23/14.29 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[422, 421])).
% 22.23/14.29 tff(424,plain,
% 22.23/14.29 (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[423, 229, 228, 32, 417])).
% 22.23/14.29 tff(425,plain,
% 22.23/14.29 (v14_lattices(A!0)),
% 22.23/14.29 inference(and_elim,[status(thm)],[31])).
% 22.23/14.29 tff(426,plain,
% 22.23/14.29 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | (~v14_lattices(A!0)) | v13_lattices(k1_lattice2(A!0))),
% 22.23/14.29 inference(tautology,[status(thm)],[])).
% 22.23/14.29 tff(427,plain,
% 22.23/14.29 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | v13_lattices(k1_lattice2(A!0))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[426, 425])).
% 22.23/14.29 tff(428,plain,
% 22.23/14.29 (v13_lattices(k1_lattice2(A!0))),
% 22.23/14.29 inference(unit_resolution,[status(thm)],[427, 424])).
% 22.23/14.29 tff(429,plain,
% 22.23/14.29 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[428, 404])).
% 22.23/14.29 tff(430,plain,
% 22.23/14.29 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(431,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[430])).
% 22.23/14.29 tff(432,plain,
% 22.23/14.29 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(433,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[432])).
% 22.23/14.29 tff(434,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 22.23/14.29 inference(transitivity,[status(thm)],[433, 431])).
% 22.23/14.29 tff(435,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))) <=> (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))), (((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), rewrite(((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))) <=> ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))), (((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))), (![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(436,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[435])).
% 22.23/14.29 tff(437,plain,
% 22.23/14.29 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~(B = u1_struct_0(A)))) <=> (B = u1_struct_0(A))), (((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ((B = u1_struct_0(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))), rewrite(((B = u1_struct_0(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ((B = u1_struct_0(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ((B = u1_struct_0(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))), (((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ((~m1_filter_0(B, A)) | ((B = u1_struct_0(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))))), rewrite(((~m1_filter_0(B, A)) | ((B = u1_struct_0(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (~v13_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) | (~v13_lattices(A))))), rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) | (~v13_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (~v13_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(438,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (~v13_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[437])).
% 22.23/14.29 tff(439,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A)))),
% 22.23/14.29 inference(rewrite,[status(thm)],[])).
% 22.23/14.29 tff(440,plain,
% 22.23/14.29 (^[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(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A)))))) <=> (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))), ((m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) <=> (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))), rewrite((m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) <=> ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))), ((m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) <=> ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))))), (![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))), ((v13_lattices(A) => ![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))) <=> (v13_lattices(A) => ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))))), rewrite((v13_lattices(A) => ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))) <=> ((~v13_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))), ((v13_lattices(A) => ![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))) <=> ((~v13_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) => ![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v13_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v13_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) => ![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A)))))),
% 22.23/14.29 inference(bind,[status(th)],[])).
% 22.23/14.29 tff(441,plain,
% 22.23/14.29 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) => ![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A)))),
% 22.23/14.29 inference(quant_intro,[status(thm)],[440])).
% 22.23/14.29 tff(442,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) => ![B: $i] : (m1_filter_0(B, A) => (~((~(B = u1_struct_0(A))) & ![C: $i] : (m1_filter_0(C, A) => (~(r1_tarski(B, C) & v1_filter_0(C, A)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t22_filter_0')).
% 22.23/14.29 tff(443,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[442, 441])).
% 22.23/14.29 tff(444,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~((~(B = u1_struct_0(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r1_tarski(B, C) & v1_filter_0(C, A))))))) | (~v13_lattices(A)))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[443, 439])).
% 22.23/14.29 tff(445,plain,(
% 22.23/14.29 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~(~(B = u1_struct_0(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (~v13_lattices(A)))),
% 22.23/14.29 inference(skolemize,[status(sab)],[444])).
% 22.23/14.29 tff(446,plain,
% 22.23/14.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~v13_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r1_tarski(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[445, 438])).
% 22.23/14.29 tff(447,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[446, 436])).
% 22.23/14.29 tff(448,plain,
% 22.23/14.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 22.23/14.29 inference(modus_ponens,[status(thm)],[447, 434])).
% 22.23/14.29 tff(449,plain,
% 22.23/14.29 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.30 inference(rewrite,[status(thm)],[])).
% 22.23/14.30 tff(450,plain,
% 22.23/14.30 ((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)))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.30 inference(rewrite,[status(thm)],[])).
% 22.23/14.30 tff(451,plain,
% 22.23/14.30 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 22.23/14.30 inference(monotonicity,[status(thm)],[450])).
% 22.23/14.30 tff(452,plain,
% 22.23/14.30 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.30 inference(transitivity,[status(thm)],[451, 449])).
% 22.23/14.30 tff(453,plain,
% 22.23/14.30 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.30 inference(quant_inst,[status(thm)],[])).
% 22.23/14.30 tff(454,plain,
% 22.23/14.30 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v13_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((B = u1_struct_0(A)) | (~m1_filter_0(B, A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r1_tarski(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(modus_ponens,[status(thm)],[453, 452])).
% 22.23/14.30 tff(455,plain,
% 22.23/14.30 ((~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))) | (~v13_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] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(unit_resolution,[status(thm)],[454, 448])).
% 22.23/14.30 tff(456,plain,
% 22.23/14.30 (![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(unit_resolution,[status(thm)],[455, 429, 157, 241, 236])).
% 22.23/14.30 tff(457,plain,
% 22.23/14.30 (((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(rewrite,[status(thm)],[])).
% 22.23/14.30 tff(458,plain,
% 22.23/14.30 (((k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(rewrite,[status(thm)],[])).
% 22.23/14.30 tff(459,plain,
% 22.23/14.30 (((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.30 inference(monotonicity,[status(thm)],[458])).
% 22.23/14.30 tff(460,plain,
% 22.23/14.30 (((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(transitivity,[status(thm)],[459, 457])).
% 22.23/14.30 tff(461,plain,
% 22.23/14.30 ((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.30 inference(quant_inst,[status(thm)],[])).
% 22.23/14.30 tff(462,plain,
% 22.23/14.30 ((~![B: $i] : ((B = u1_struct_0(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_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.23/14.30 inference(modus_ponens,[status(thm)],[461, 460])).
% 22.23/14.30 tff(463,plain,
% 22.23/14.30 ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k7_filter_2(A!0, B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.23/14.30 inference(unit_resolution,[status(thm)],[462, 456])).
% 22.23/14.30 tff(464,plain,
% 22.23/14.30 (~((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.23/14.30 inference(unit_resolution,[status(thm)],[463, 402, 314])).
% 22.23/14.30 tff(465,plain,
% 22.23/14.30 (((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.30 inference(tautology,[status(thm)],[])).
% 22.23/14.30 tff(466,plain,
% 22.23/14.30 (m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.23/14.30 inference(unit_resolution,[status(thm)],[465, 464])).
% 22.23/14.30 tff(467,plain,
% 22.23/14.30 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 22.23/14.30 inference(bind,[status(th)],[])).
% 22.23/14.30 tff(468,plain,
% 22.23/14.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.30 inference(quant_intro,[status(thm)],[467])).
% 22.23/14.30 tff(469,plain,
% 22.23/14.30 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 22.23/14.30 inference(bind,[status(th)],[])).
% 22.23/14.30 tff(470,plain,
% 22.23/14.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.30 inference(quant_intro,[status(thm)],[469])).
% 22.23/14.30 tff(471,plain,
% 22.23/14.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.30 inference(transitivity,[status(thm)],[470, 468])).
% 22.23/14.30 tff(472,plain,
% 22.23/14.30 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 22.23/14.30 inference(bind,[status(th)],[])).
% 22.23/14.30 tff(473,plain,
% 22.23/14.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.30 inference(quant_intro,[status(thm)],[472])).
% 22.23/14.30 tff(474,plain,
% 22.23/14.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 22.23/14.30 inference(rewrite,[status(thm)],[])).
% 22.23/14.30 tff(475,plain,
% 22.23/14.30 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.31 inference(bind,[status(th)],[])).
% 22.23/14.31 tff(476,plain,
% 22.23/14.31 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 22.23/14.31 inference(quant_intro,[status(thm)],[475])).
% 22.23/14.31 tff(477,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 22.23/14.31 tff(478,plain,
% 22.23/14.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[477, 476])).
% 22.23/14.31 tff(479,plain,
% 22.23/14.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[478, 474])).
% 22.23/14.31 tff(480,plain,(
% 22.23/14.31 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 22.23/14.31 inference(skolemize,[status(sab)],[479])).
% 22.23/14.31 tff(481,plain,
% 22.23/14.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[480, 473])).
% 22.23/14.31 tff(482,plain,
% 22.23/14.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[481, 471])).
% 22.23/14.31 tff(483,plain,
% 22.23/14.31 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 22.23/14.31 inference(rewrite,[status(thm)],[])).
% 22.23/14.31 tff(484,plain,
% 22.23/14.31 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 22.23/14.31 inference(quant_inst,[status(thm)],[])).
% 22.23/14.31 tff(485,plain,
% 22.23/14.31 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[484, 483])).
% 22.23/14.31 tff(486,plain,
% 22.23/14.31 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 22.23/14.31 inference(unit_resolution,[status(thm)],[485, 482])).
% 22.23/14.31 tff(487,plain,
% 22.23/14.31 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 22.23/14.31 inference(unit_resolution,[status(thm)],[486, 241, 157, 236])).
% 22.23/14.31 tff(488,plain,
% 22.23/14.31 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 22.23/14.31 inference(rewrite,[status(thm)],[])).
% 22.23/14.31 tff(489,plain,
% 22.23/14.31 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 22.23/14.31 inference(quant_inst,[status(thm)],[])).
% 22.23/14.31 tff(490,plain,
% 22.23/14.31 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[489, 488])).
% 22.23/14.31 tff(491,plain,
% 22.23/14.31 (~(v1_xboole_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.23/14.31 inference(unit_resolution,[status(thm)],[490, 487, 466])).
% 22.23/14.31 tff(492,plain,
% 22.23/14.31 ((v1_xboole_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.23/14.31 inference(tautology,[status(thm)],[])).
% 22.23/14.31 tff(493,plain,
% 22.23/14.31 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.23/14.31 inference(unit_resolution,[status(thm)],[492, 491])).
% 22.23/14.31 tff(494,plain,
% 22.23/14.31 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 22.23/14.31 inference(modus_ponens,[status(thm)],[493, 211])).
% 22.23/14.31 tff(495,plain,
% 22.23/14.31 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.23/14.31 inference(rewrite,[status(thm)],[])).
% 22.23/14.31 tff(496,plain,
% 22.23/14.31 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.31 inference(quant_inst,[status(thm)],[])).
% 22.34/14.31 tff(497,plain,
% 22.34/14.31 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[496, 495])).
% 22.34/14.31 tff(498,plain,
% 22.34/14.31 ((~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.31 inference(unit_resolution,[status(thm)],[497, 392])).
% 22.34/14.31 tff(499,plain,
% 22.34/14.31 (k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.31 inference(unit_resolution,[status(thm)],[498, 494])).
% 22.34/14.31 tff(500,plain,
% 22.34/14.31 (m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)) <=> m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.31 inference(monotonicity,[status(thm)],[36])).
% 22.34/14.31 tff(501,plain,
% 22.34/14.31 (m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 22.34/14.31 inference(symmetry,[status(thm)],[500])).
% 22.34/14.31 tff(502,plain,
% 22.34/14.31 (m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[466, 501])).
% 22.34/14.31 tff(503,plain,
% 22.34/14.31 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(504,plain,
% 22.34/14.31 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[503])).
% 22.34/14.31 tff(505,plain,
% 22.34/14.31 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(506,plain,
% 22.34/14.31 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[505])).
% 22.34/14.31 tff(507,plain,
% 22.34/14.31 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 22.34/14.31 inference(rewrite,[status(thm)],[])).
% 22.34/14.31 tff(508,plain,
% 22.34/14.31 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(509,plain,
% 22.34/14.31 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[508])).
% 22.34/14.31 tff(510,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k14_filter_2')).
% 22.34/14.31 tff(511,plain,
% 22.34/14.31 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[510, 509])).
% 22.34/14.31 tff(512,plain,
% 22.34/14.31 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[511, 507])).
% 22.34/14.31 tff(513,plain,(
% 22.34/14.31 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 22.34/14.31 inference(skolemize,[status(sab)],[512])).
% 22.34/14.31 tff(514,plain,
% 22.34/14.31 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[513, 506])).
% 22.34/14.31 tff(515,plain,
% 22.34/14.31 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[514, 504])).
% 22.34/14.31 tff(516,plain,
% 22.34/14.31 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.31 inference(rewrite,[status(thm)],[])).
% 22.34/14.31 tff(517,plain,
% 22.34/14.31 ((v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.31 inference(rewrite,[status(thm)],[])).
% 22.34/14.31 tff(518,plain,
% 22.34/14.31 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.34/14.31 inference(monotonicity,[status(thm)],[517])).
% 22.34/14.31 tff(519,plain,
% 22.34/14.31 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.31 inference(transitivity,[status(thm)],[518, 516])).
% 22.34/14.31 tff(520,plain,
% 22.34/14.31 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 22.34/14.31 inference(quant_inst,[status(thm)],[])).
% 22.34/14.31 tff(521,plain,
% 22.34/14.31 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[520, 519])).
% 22.34/14.31 tff(522,plain,
% 22.34/14.31 ((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.31 inference(unit_resolution,[status(thm)],[521, 229, 228, 32, 515])).
% 22.34/14.31 tff(523,plain,
% 22.34/14.31 (k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.31 inference(unit_resolution,[status(thm)],[522, 502])).
% 22.34/14.31 tff(524,plain,
% 22.34/14.31 (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.31 inference(symmetry,[status(thm)],[523])).
% 22.34/14.31 tff(525,plain,
% 22.34/14.31 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.31 inference(monotonicity,[status(thm)],[40])).
% 22.34/14.31 tff(526,plain,
% 22.34/14.31 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 22.34/14.31 inference(symmetry,[status(thm)],[525])).
% 22.34/14.31 tff(527,plain,
% 22.34/14.31 (m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[493, 526])).
% 22.34/14.31 tff(528,plain,
% 22.34/14.31 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(529,plain,
% 22.34/14.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[528])).
% 22.34/14.31 tff(530,plain,
% 22.34/14.31 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(531,plain,
% 22.34/14.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[530])).
% 22.34/14.31 tff(532,plain,
% 22.34/14.31 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(533,plain,
% 22.34/14.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[532])).
% 22.34/14.31 tff(534,plain,
% 22.34/14.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.34/14.31 inference(transitivity,[status(thm)],[533, 531])).
% 22.34/14.31 tff(535,plain,
% 22.34/14.31 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(536,plain,
% 22.34/14.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[535])).
% 22.34/14.31 tff(537,plain,
% 22.34/14.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.31 inference(rewrite,[status(thm)],[])).
% 22.34/14.31 tff(538,plain,
% 22.34/14.31 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))))),
% 22.34/14.31 inference(bind,[status(th)],[])).
% 22.34/14.31 tff(539,plain,
% 22.34/14.31 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.31 inference(quant_intro,[status(thm)],[538])).
% 22.34/14.31 tff(540,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_filter_2')).
% 22.34/14.31 tff(541,plain,
% 22.34/14.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.31 inference(modus_ponens,[status(thm)],[540, 539])).
% 22.34/14.32 tff(542,plain,
% 22.34/14.32 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[541, 537])).
% 22.34/14.32 tff(543,plain,(
% 22.34/14.32 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.32 inference(skolemize,[status(sab)],[542])).
% 22.34/14.32 tff(544,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[543, 536])).
% 22.34/14.32 tff(545,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[544, 534])).
% 22.34/14.32 tff(546,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[545, 529])).
% 22.34/14.32 tff(547,plain,
% 22.34/14.32 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(548,plain,
% 22.34/14.32 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 22.34/14.32 inference(quant_inst,[status(thm)],[])).
% 22.34/14.32 tff(549,plain,
% 22.34/14.32 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[548, 547])).
% 22.34/14.32 tff(550,plain,
% 22.34/14.32 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[549, 229, 228, 32, 546])).
% 22.34/14.32 tff(551,plain,
% 22.34/14.32 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(552,plain,
% 22.34/14.32 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.32 inference(quant_inst,[status(thm)],[])).
% 22.34/14.32 tff(553,plain,
% 22.34/14.32 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[552, 551])).
% 22.34/14.32 tff(554,plain,
% 22.34/14.32 ((~m1_subset_1(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[553, 550])).
% 22.34/14.32 tff(555,plain,
% 22.34/14.32 (k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[554, 527])).
% 22.34/14.32 tff(556,plain,
% 22.34/14.32 (tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k8_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.32 inference(symmetry,[status(thm)],[555])).
% 22.34/14.32 tff(557,plain,
% 22.34/14.32 (tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.32 inference(transitivity,[status(thm)],[556, 524])).
% 22.34/14.32 tff(558,plain,
% 22.34/14.32 (m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0) <=> m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 22.34/14.32 inference(monotonicity,[status(thm)],[557])).
% 22.34/14.32 tff(559,plain,
% 22.34/14.32 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) <=> m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 22.34/14.32 inference(symmetry,[status(thm)],[558])).
% 22.34/14.32 tff(560,plain,
% 22.34/14.32 (^[A: $i, B: $i] : refl((m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 22.34/14.32 inference(bind,[status(th)],[])).
% 22.34/14.32 tff(561,plain,
% 22.34/14.32 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.32 inference(quant_intro,[status(thm)],[560])).
% 22.34/14.32 tff(562,plain,
% 22.34/14.32 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 22.34/14.32 inference(bind,[status(th)],[])).
% 22.34/14.32 tff(563,plain,
% 22.34/14.32 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.32 inference(quant_intro,[status(thm)],[562])).
% 22.34/14.32 tff(564,plain,
% 22.34/14.32 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(565,plain,
% 22.34/14.32 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))))),
% 22.34/14.32 inference(bind,[status(th)],[])).
% 22.34/14.32 tff(566,plain,
% 22.34/14.32 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 22.34/14.32 inference(quant_intro,[status(thm)],[565])).
% 22.34/14.32 tff(567,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k14_filter_2')).
% 22.34/14.32 tff(568,plain,
% 22.34/14.32 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[567, 566])).
% 22.34/14.32 tff(569,plain,
% 22.34/14.32 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[568, 564])).
% 22.34/14.32 tff(570,plain,(
% 22.34/14.32 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 22.34/14.32 inference(skolemize,[status(sab)],[569])).
% 22.34/14.32 tff(571,plain,
% 22.34/14.32 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[570, 563])).
% 22.34/14.32 tff(572,plain,
% 22.34/14.32 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[571, 561])).
% 22.34/14.32 tff(573,plain,
% 22.34/14.32 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(574,plain,
% 22.34/14.32 ((m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(575,plain,
% 22.34/14.32 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))))),
% 22.34/14.32 inference(monotonicity,[status(thm)],[574])).
% 22.34/14.32 tff(576,plain,
% 22.34/14.32 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 22.34/14.32 inference(transitivity,[status(thm)],[575, 573])).
% 22.34/14.32 tff(577,plain,
% 22.34/14.32 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 22.34/14.32 inference(quant_inst,[status(thm)],[])).
% 22.34/14.32 tff(578,plain,
% 22.34/14.32 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[577, 576])).
% 22.34/14.32 tff(579,plain,
% 22.34/14.32 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[578, 229, 228, 32, 572])).
% 22.34/14.32 tff(580,plain,
% 22.34/14.32 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[579, 502])).
% 22.34/14.32 tff(581,plain,
% 22.34/14.32 (m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[580, 559])).
% 22.34/14.32 tff(582,plain,
% 22.34/14.32 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(583,plain,
% 22.34/14.32 ((v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.32 inference(rewrite,[status(thm)],[])).
% 22.34/14.32 tff(584,plain,
% 22.34/14.32 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 22.34/14.32 inference(monotonicity,[status(thm)],[583])).
% 22.34/14.32 tff(585,plain,
% 22.34/14.32 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.32 inference(transitivity,[status(thm)],[584, 582])).
% 22.34/14.32 tff(586,plain,
% 22.34/14.32 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 22.34/14.32 inference(quant_inst,[status(thm)],[])).
% 22.34/14.32 tff(587,plain,
% 22.34/14.32 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[586, 585])).
% 22.34/14.32 tff(588,plain,
% 22.34/14.32 (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[587, 229, 228, 32, 280, 581])).
% 22.34/14.32 tff(589,plain,
% 22.34/14.32 (k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.32 inference(transitivity,[status(thm)],[588, 499])).
% 22.34/14.32 tff(590,plain,
% 22.34/14.32 (v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)) <=> v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.32 inference(monotonicity,[status(thm)],[589, 36])).
% 22.34/14.32 tff(591,plain,
% 22.34/14.32 (v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 22.34/14.32 inference(symmetry,[status(thm)],[590])).
% 22.34/14.32 tff(592,plain,
% 22.34/14.32 (((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.32 inference(tautology,[status(thm)],[])).
% 22.34/14.32 tff(593,plain,
% 22.34/14.32 (v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 22.34/14.32 inference(unit_resolution,[status(thm)],[592, 464])).
% 22.34/14.32 tff(594,plain,
% 22.34/14.32 (v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 22.34/14.32 inference(modus_ponens,[status(thm)],[593, 591])).
% 22.34/14.32 tff(595,plain,
% 22.34/14.32 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))),
% 22.34/14.32 inference(bind,[status(th)],[])).
% 22.34/14.32 tff(596,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.32 inference(quant_intro,[status(thm)],[595])).
% 22.34/14.32 tff(597,plain,
% 22.34/14.32 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 22.34/14.32 inference(bind,[status(th)],[])).
% 22.34/14.32 tff(598,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 22.34/14.32 inference(quant_intro,[status(thm)],[597])).
% 22.34/14.32 tff(599,plain,
% 22.34/14.32 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 22.34/14.32 inference(bind,[status(th)],[])).
% 22.34/14.32 tff(600,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 22.34/14.32 inference(quant_intro,[status(thm)],[599])).
% 22.34/14.32 tff(601,plain,
% 22.34/14.32 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 22.34/14.32 inference(transitivity,[status(thm)],[600, 598])).
% 22.34/14.32 tff(602,plain,
% 22.34/14.32 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))))),
% 22.34/14.33 inference(bind,[status(th)],[])).
% 22.34/14.33 tff(603,plain,
% 22.34/14.33 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 22.34/14.33 inference(quant_intro,[status(thm)],[602])).
% 22.34/14.33 tff(604,plain,
% 22.34/14.33 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.33 inference(rewrite,[status(thm)],[])).
% 22.34/14.33 tff(605,plain,
% 22.34/14.33 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))))),
% 22.34/14.33 inference(bind,[status(th)],[])).
% 22.34/14.33 tff(606,plain,
% 22.34/14.33 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.33 inference(quant_intro,[status(thm)],[605])).
% 22.34/14.33 tff(607,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_filter_2')).
% 22.34/14.33 tff(608,plain,
% 22.34/14.33 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[607, 606])).
% 22.34/14.33 tff(609,plain,
% 22.34/14.33 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[608, 604])).
% 22.34/14.33 tff(610,plain,(
% 22.34/14.33 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.33 inference(skolemize,[status(sab)],[609])).
% 22.34/14.33 tff(611,plain,
% 22.34/14.33 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[610, 603])).
% 22.34/14.33 tff(612,plain,
% 22.34/14.33 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[611, 601])).
% 22.34/14.33 tff(613,plain,
% 22.34/14.33 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[612, 596])).
% 22.34/14.33 tff(614,plain,
% 22.34/14.33 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 22.34/14.33 inference(rewrite,[status(thm)],[])).
% 22.34/14.33 tff(615,plain,
% 22.34/14.33 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 22.34/14.33 inference(quant_inst,[status(thm)],[])).
% 22.34/14.33 tff(616,plain,
% 22.34/14.33 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[615, 614])).
% 22.34/14.33 tff(617,plain,
% 22.34/14.33 (![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 22.34/14.33 inference(unit_resolution,[status(thm)],[616, 229, 228, 32, 613])).
% 22.34/14.33 tff(618,plain,
% 22.34/14.33 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 22.34/14.33 inference(rewrite,[status(thm)],[])).
% 22.34/14.33 tff(619,plain,
% 22.34/14.33 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 22.34/14.33 inference(quant_inst,[status(thm)],[])).
% 22.34/14.33 tff(620,plain,
% 22.34/14.33 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[619, 618])).
% 22.34/14.33 tff(621,plain,
% 22.34/14.33 (r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 22.34/14.33 inference(unit_resolution,[status(thm)],[620, 617, 581])).
% 22.34/14.33 tff(622,plain,
% 22.34/14.33 (B!1 = k7_filter_2(A!0, B!1)),
% 22.34/14.33 inference(symmetry,[status(thm)],[397])).
% 22.34/14.33 tff(623,plain,
% 22.34/14.33 (r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.33 inference(monotonicity,[status(thm)],[622])).
% 22.34/14.33 tff(624,plain,
% 22.34/14.33 (r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.33 inference(symmetry,[status(thm)],[623])).
% 22.34/14.33 tff(625,plain,
% 22.34/14.33 (((~m1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.33 inference(tautology,[status(thm)],[])).
% 22.34/14.33 tff(626,plain,
% 22.34/14.33 (r1_tarski(k7_filter_2(A!0, B!1), tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.33 inference(unit_resolution,[status(thm)],[625, 464])).
% 22.34/14.33 tff(627,plain,
% 22.34/14.33 (r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[626, 624])).
% 22.34/14.33 tff(628,plain,
% 22.34/14.33 (^[C: $i] : refl(((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))) <=> ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))))),
% 22.34/14.33 inference(bind,[status(th)],[])).
% 22.34/14.33 tff(629,plain,
% 22.34/14.33 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))) <=> ![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 22.34/14.33 inference(quant_intro,[status(thm)],[628])).
% 22.34/14.33 tff(630,plain,
% 22.34/14.33 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1_tarski(B!1, C) & r2_filter_2(A!0, C)) <=> (~((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))))), ((~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))) <=> (~(~((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))))))), rewrite((~(~((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))))) <=> ((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))), ((~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))) <=> ((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C))))), (((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | ((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))))), rewrite(((~m2_filter_2(C, A!0)) | ((~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))), (((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))))),
% 22.34/14.33 inference(bind,[status(th)],[])).
% 22.34/14.33 tff(631,plain,
% 22.34/14.33 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C)))) <=> ![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 22.34/14.33 inference(quant_intro,[status(thm)],[630])).
% 22.34/14.33 tff(632,plain,
% 22.34/14.33 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r1_tarski(B!1, C) & r2_filter_2(A!0, C))))),
% 22.34/14.33 inference(and_elim,[status(thm)],[31])).
% 22.34/14.33 tff(633,plain,
% 22.34/14.33 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[632, 631])).
% 22.34/14.33 tff(634,plain,
% 22.34/14.33 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 22.34/14.33 inference(modus_ponens,[status(thm)],[633, 629])).
% 22.34/14.33 tff(635,plain,
% 22.34/14.33 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.33 inference(rewrite,[status(thm)],[])).
% 22.34/14.33 tff(636,plain,
% 22.34/14.33 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 22.34/14.37 inference(quant_inst,[status(thm)],[])).
% 22.34/14.37 tff(637,plain,
% 22.34/14.37 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r1_tarski(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.37 inference(modus_ponens,[status(thm)],[636, 635])).
% 22.34/14.37 tff(638,plain,
% 22.34/14.37 ((~m2_filter_2(tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r1_tarski(B!1, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 22.34/14.37 inference(unit_resolution,[status(thm)],[637, 634])).
% 22.34/14.37 tff(639,plain,
% 22.34/14.37 (~r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 22.34/14.37 inference(unit_resolution,[status(thm)],[638, 581, 627])).
% 22.34/14.37 tff(640,plain,
% 22.34/14.37 ((~(r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | r2_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 22.34/14.37 inference(tautology,[status(thm)],[])).
% 22.34/14.37 tff(641,plain,
% 22.34/14.37 (~v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 22.34/14.37 inference(unit_resolution,[status(thm)],[640, 639, 621])).
% 22.34/14.37 tff(642,plain,
% 22.34/14.37 ($false),
% 22.34/14.37 inference(unit_resolution,[status(thm)],[641, 594])).
% 22.34/14.37 % SZS output end Proof
%------------------------------------------------------------------------------