TSTP Solution File: LAT286+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT286+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 18:32:41 EDT 2022
% Result : Theorem 243.47s 155.63s
% Output : Proof 244.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT286+1 : TPTP v8.1.0. Released v3.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 13:05:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 243.47/155.63 % SZS status Theorem
% 243.47/155.63 % SZS output start Proof
% 243.47/155.63 tff(m1_subset_1_type, type, (
% 243.47/155.63 m1_subset_1: ( $i * $i ) > $o)).
% 243.47/155.63 tff(u1_struct_0_type, type, (
% 243.47/155.63 u1_struct_0: $i > $i)).
% 243.47/155.63 tff(k6_lopclset_type, type, (
% 243.47/155.63 k6_lopclset: $i > $i)).
% 243.47/155.63 tff(tptp_fun_A_0_type, type, (
% 243.47/155.63 tptp_fun_A_0: $i)).
% 243.47/155.63 tff(k2_pre_topc_type, type, (
% 243.47/155.63 k2_pre_topc: $i > $i)).
% 243.47/155.63 tff(a_1_0_lopclset_type, type, (
% 243.47/155.63 a_1_0_lopclset: $i > $i)).
% 243.47/155.63 tff(u1_lattices_type, type, (
% 243.47/155.63 u1_lattices: $i > $i)).
% 243.47/155.63 tff(k5_lopclset_type, type, (
% 243.47/155.63 k5_lopclset: $i > $i)).
% 243.47/155.63 tff(u2_lattices_type, type, (
% 243.47/155.63 u2_lattices: $i > $i)).
% 243.47/155.63 tff(k4_lopclset_type, type, (
% 243.47/155.63 k4_lopclset: $i > $i)).
% 243.47/155.63 tff(g3_lattices_type, type, (
% 243.47/155.63 g3_lattices: ( $i * $i * $i ) > $i)).
% 243.47/155.63 tff(l3_lattices_type, type, (
% 243.47/155.63 l3_lattices: $i > $o)).
% 243.47/155.63 tff(v10_lattices_type, type, (
% 243.47/155.63 v10_lattices: $i > $o)).
% 243.47/155.63 tff(v3_struct_0_type, type, (
% 243.47/155.63 v3_struct_0: $i > $o)).
% 243.47/155.63 tff(v2_pre_topc_type, type, (
% 243.47/155.63 v2_pre_topc: $i > $o)).
% 243.47/155.63 tff(l1_pre_topc_type, type, (
% 243.47/155.63 l1_pre_topc: $i > $o)).
% 243.47/155.63 tff(v3_lattices_type, type, (
% 243.47/155.63 v3_lattices: $i > $o)).
% 243.47/155.63 tff(k1_lopclset_type, type, (
% 243.47/155.63 k1_lopclset: $i > $i)).
% 243.47/155.63 tff(m1_relset_1_type, type, (
% 243.47/155.63 m1_relset_1: ( $i * $i * $i ) > $o)).
% 243.47/155.63 tff(k2_zfmisc_1_type, type, (
% 243.47/155.63 k2_zfmisc_1: ( $i * $i ) > $i)).
% 243.47/155.63 tff(m2_relset_1_type, type, (
% 243.47/155.63 m2_relset_1: ( $i * $i * $i ) > $o)).
% 243.47/155.63 tff(v1_funct_2_type, type, (
% 243.47/155.63 v1_funct_2: ( $i * $i * $i ) > $o)).
% 243.47/155.63 tff(v1_funct_1_type, type, (
% 243.47/155.63 v1_funct_1: $i > $o)).
% 243.47/155.63 tff(m2_subset_1_type, type, (
% 243.47/155.63 m2_subset_1: ( $i * $i * $i ) > $o)).
% 243.47/155.63 tff(k1_zfmisc_1_type, type, (
% 243.47/155.63 k1_zfmisc_1: $i > $i)).
% 243.47/155.63 tff(v1_xboole_0_type, type, (
% 243.47/155.63 v1_xboole_0: $i > $o)).
% 243.47/155.63 tff(v4_finsub_1_type, type, (
% 243.47/155.63 v4_finsub_1: $i > $o)).
% 243.47/155.63 tff(v3_finsub_1_type, type, (
% 243.47/155.63 v3_finsub_1: $i > $o)).
% 243.47/155.63 tff(v1_finsub_1_type, type, (
% 243.47/155.63 v1_finsub_1: $i > $o)).
% 243.47/155.63 tff(1,plain,
% 243.47/155.63 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(2,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[1])).
% 243.47/155.63 tff(3,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite(((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))) <=> (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(4,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[3])).
% 243.47/155.63 tff(5,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(6,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), rewrite((((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A))) <=> ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(7,plain,
% 243.47/155.63 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[6])).
% 243.47/155.63 tff(8,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_lopclset')).
% 243.47/155.63 tff(9,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[8, 7])).
% 243.47/155.63 tff(10,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[9, 5])).
% 243.47/155.63 tff(11,plain,(
% 243.47/155.63 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 243.47/155.63 inference(skolemize,[status(sab)],[10])).
% 243.47/155.63 tff(12,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[11, 4])).
% 243.47/155.63 tff(13,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[12, 2])).
% 243.47/155.63 tff(14,plain,
% 243.47/155.63 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A)))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(15,plain,
% 243.47/155.63 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A)))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(16,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_lopclset')).
% 243.47/155.63 tff(17,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[16, 15])).
% 243.47/155.63 tff(18,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[17, 14])).
% 243.47/155.63 tff(19,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[18, 14])).
% 243.47/155.63 tff(20,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[19, 14])).
% 243.47/155.63 tff(21,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[20, 14])).
% 243.47/155.63 tff(22,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[21, 14])).
% 243.47/155.63 tff(23,plain,
% 243.47/155.63 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[22, 14])).
% 243.47/155.63 tff(24,plain,(
% 243.47/155.63 ~((~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0))) | m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))))),
% 243.47/155.63 inference(skolemize,[status(sab)],[23])).
% 243.47/155.63 tff(25,plain,
% 243.47/155.63 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)),
% 243.47/155.63 inference(or_elim,[status(thm)],[24])).
% 243.47/155.63 tff(26,plain,
% 243.47/155.63 (l1_pre_topc(A!0)),
% 243.47/155.63 inference(and_elim,[status(thm)],[25])).
% 243.47/155.63 tff(27,plain,
% 243.47/155.63 (v2_pre_topc(A!0)),
% 243.47/155.63 inference(and_elim,[status(thm)],[25])).
% 243.47/155.63 tff(28,plain,
% 243.47/155.63 (~v3_struct_0(A!0)),
% 243.47/155.63 inference(and_elim,[status(thm)],[25])).
% 243.47/155.63 tff(29,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(30,plain,
% 243.47/155.63 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0)))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(31,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0)))))))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[30])).
% 243.47/155.63 tff(32,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))),
% 243.47/155.63 inference(transitivity,[status(thm)],[31, 29])).
% 243.47/155.63 tff(33,plain,
% 243.47/155.63 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))))),
% 243.47/155.63 inference(quant_inst,[status(thm)],[])).
% 243.47/155.63 tff(34,plain,
% 243.47/155.63 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0)))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[33, 32])).
% 243.47/155.63 tff(35,plain,
% 243.47/155.63 (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))),
% 243.47/155.63 inference(unit_resolution,[status(thm)],[34, 28, 27, 26, 13])).
% 243.47/155.63 tff(36,plain,
% 243.47/155.63 ((v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0)))) | l3_lattices(k6_lopclset(A!0))),
% 243.47/155.63 inference(tautology,[status(thm)],[])).
% 243.47/155.63 tff(37,plain,
% 243.47/155.63 (l3_lattices(k6_lopclset(A!0))),
% 243.47/155.63 inference(unit_resolution,[status(thm)],[36, 35])).
% 243.47/155.63 tff(38,plain,
% 243.47/155.63 (^[A: $i] : refl((v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(39,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[38])).
% 243.47/155.63 tff(40,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(41,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[40])).
% 243.47/155.63 tff(42,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(43,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(44,plain,
% 243.47/155.63 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[43])).
% 243.47/155.63 tff(45,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_lopclset')).
% 243.47/155.63 tff(46,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[45, 44])).
% 243.47/155.63 tff(47,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[46, 42])).
% 243.47/155.63 tff(48,plain,(
% 243.47/155.63 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 243.47/155.63 inference(skolemize,[status(sab)],[47])).
% 243.47/155.63 tff(49,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[48, 41])).
% 243.47/155.63 tff(50,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[49, 39])).
% 243.47/155.63 tff(51,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(52,plain,
% 243.47/155.63 ((v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(53,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[52])).
% 243.47/155.63 tff(54,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))),
% 243.47/155.63 inference(transitivity,[status(thm)],[53, 51])).
% 243.47/155.63 tff(55,plain,
% 243.47/155.63 ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 243.47/155.63 inference(quant_inst,[status(thm)],[])).
% 243.47/155.63 tff(56,plain,
% 243.47/155.63 ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[55, 54])).
% 243.47/155.63 tff(57,plain,
% 243.47/155.63 (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))),
% 243.47/155.63 inference(unit_resolution,[status(thm)],[56, 28, 27, 26, 50])).
% 243.47/155.63 tff(58,plain,
% 243.47/155.63 (g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = k6_lopclset(A!0)),
% 243.47/155.63 inference(symmetry,[status(thm)],[57])).
% 243.47/155.63 tff(59,plain,
% 243.47/155.63 (^[A: $i] : refl((v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A))) <=> (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(60,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[59])).
% 243.47/155.63 tff(61,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(62,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[61])).
% 243.47/155.63 tff(63,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(64,plain,
% 243.47/155.63 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(65,plain,
% 243.47/155.63 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[64])).
% 243.47/155.63 tff(66,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => (k1_lopclset(A) = a_1_0_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_lopclset')).
% 243.47/155.63 tff(67,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[66, 65])).
% 243.47/155.63 tff(68,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[67, 63])).
% 243.47/155.63 tff(69,plain,(
% 243.47/155.63 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 243.47/155.63 inference(skolemize,[status(sab)],[68])).
% 243.47/155.63 tff(70,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[69, 62])).
% 243.47/155.63 tff(71,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[70, 60])).
% 243.47/155.63 tff(72,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(73,plain,
% 243.47/155.63 ((v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(74,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0))))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[73])).
% 243.47/155.63 tff(75,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))),
% 243.47/155.63 inference(transitivity,[status(thm)],[74, 72])).
% 243.47/155.63 tff(76,plain,
% 243.47/155.63 ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0)))),
% 243.47/155.63 inference(quant_inst,[status(thm)],[])).
% 243.47/155.63 tff(77,plain,
% 243.47/155.63 ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[76, 75])).
% 243.47/155.63 tff(78,plain,
% 243.47/155.63 (k1_lopclset(A!0) = a_1_0_lopclset(A!0)),
% 243.47/155.63 inference(unit_resolution,[status(thm)],[77, 28, 26, 71])).
% 243.47/155.63 tff(79,plain,
% 243.47/155.63 (a_1_0_lopclset(A!0) = k1_lopclset(A!0)),
% 243.47/155.63 inference(symmetry,[status(thm)],[78])).
% 243.47/155.63 tff(80,plain,
% 243.47/155.63 (g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[79])).
% 243.47/155.63 tff(81,plain,
% 243.47/155.63 (g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = k6_lopclset(A!0)),
% 243.47/155.63 inference(transitivity,[status(thm)],[80, 58])).
% 243.47/155.63 tff(82,plain,
% 243.47/155.63 (v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) <=> v3_lattices(k6_lopclset(A!0))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[81])).
% 243.47/155.63 tff(83,plain,
% 243.47/155.63 (k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)) = k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[79, 79])).
% 243.47/155.63 tff(84,plain,
% 243.47/155.63 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[83])).
% 243.47/155.63 tff(85,plain,
% 243.47/155.63 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.63 inference(symmetry,[status(thm)],[84])).
% 243.47/155.63 tff(86,plain,
% 243.47/155.63 (^[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)))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(87,plain,
% 243.47/155.63 (![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))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[86])).
% 243.47/155.63 tff(88,plain,
% 243.47/155.63 (![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))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(89,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 243.47/155.63 tff(90,plain,
% 243.47/155.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[89, 88])).
% 243.47/155.63 tff(91,plain,(
% 243.47/155.63 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 243.47/155.63 inference(skolemize,[status(sab)],[90])).
% 243.47/155.63 tff(92,plain,
% 243.47/155.63 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[91, 87])).
% 243.47/155.63 tff(93,plain,
% 243.47/155.63 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))),
% 243.47/155.63 inference(quant_inst,[status(thm)],[])).
% 243.47/155.63 tff(94,plain,
% 243.47/155.63 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.63 inference(unit_resolution,[status(thm)],[93, 92])).
% 243.47/155.63 tff(95,plain,
% 243.47/155.63 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.63 inference(monotonicity,[status(thm)],[79])).
% 243.47/155.63 tff(96,plain,
% 243.47/155.63 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.63 inference(symmetry,[status(thm)],[95])).
% 243.47/155.63 tff(97,plain,
% 243.47/155.63 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(98,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[97])).
% 243.47/155.63 tff(99,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(100,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[99])).
% 243.47/155.63 tff(101,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.63 inference(rewrite,[status(thm)],[])).
% 243.47/155.63 tff(102,plain,
% 243.47/155.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), rewrite(((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.63 inference(bind,[status(th)],[])).
% 243.47/155.63 tff(103,plain,
% 243.47/155.63 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.63 inference(quant_intro,[status(thm)],[102])).
% 243.47/155.63 tff(104,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lopclset')).
% 243.47/155.63 tff(105,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[104, 103])).
% 243.47/155.63 tff(106,plain,
% 243.47/155.63 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[105, 101])).
% 243.47/155.63 tff(107,plain,(
% 243.47/155.63 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.63 inference(skolemize,[status(sab)],[106])).
% 243.47/155.63 tff(108,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[107, 100])).
% 243.47/155.63 tff(109,plain,
% 243.47/155.63 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.63 inference(modus_ponens,[status(thm)],[108, 98])).
% 243.47/155.63 tff(110,plain,
% 243.47/155.63 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(111,plain,
% 243.47/155.64 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 243.47/155.64 inference(quant_inst,[status(thm)],[])).
% 243.47/155.64 tff(112,plain,
% 243.47/155.64 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[111, 110])).
% 243.47/155.64 tff(113,plain,
% 243.47/155.64 (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[112, 28, 27, 26, 109])).
% 243.47/155.64 tff(114,plain,
% 243.47/155.64 (((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(115,plain,
% 243.47/155.64 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[114, 113])).
% 243.47/155.64 tff(116,plain,
% 243.47/155.64 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[115, 96])).
% 243.47/155.64 tff(117,plain,
% 243.47/155.64 ((~(m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))) | m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(118,plain,
% 243.47/155.64 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[117, 116, 94])).
% 243.47/155.64 tff(119,plain,
% 243.47/155.64 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[118, 85])).
% 243.47/155.64 tff(120,plain,
% 243.47/155.64 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(monotonicity,[status(thm)],[83, 79])).
% 243.47/155.64 tff(121,plain,
% 243.47/155.64 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(symmetry,[status(thm)],[120])).
% 243.47/155.64 tff(122,plain,
% 243.47/155.64 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(123,plain,
% 243.47/155.64 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[122])).
% 243.47/155.64 tff(124,plain,
% 243.47/155.64 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(125,plain,
% 243.47/155.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[124])).
% 243.47/155.64 tff(126,plain,
% 243.47/155.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(127,plain,
% 243.47/155.64 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), rewrite(((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(128,plain,
% 243.47/155.64 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[127])).
% 243.47/155.64 tff(129,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lopclset')).
% 243.47/155.64 tff(130,plain,
% 243.47/155.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[129, 128])).
% 243.47/155.64 tff(131,plain,
% 243.47/155.64 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[130, 126])).
% 243.47/155.64 tff(132,plain,(
% 243.47/155.64 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 243.47/155.64 inference(skolemize,[status(sab)],[131])).
% 243.47/155.64 tff(133,plain,
% 243.47/155.64 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[132, 125])).
% 243.47/155.64 tff(134,plain,
% 243.47/155.64 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[133, 123])).
% 243.47/155.64 tff(135,plain,
% 243.47/155.64 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(136,plain,
% 243.47/155.64 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 243.47/155.64 inference(quant_inst,[status(thm)],[])).
% 243.47/155.64 tff(137,plain,
% 243.47/155.64 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[136, 135])).
% 243.47/155.64 tff(138,plain,
% 243.47/155.64 (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[137, 28, 27, 26, 134])).
% 243.47/155.64 tff(139,plain,
% 243.47/155.64 (((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(140,plain,
% 243.47/155.64 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[139, 138])).
% 243.47/155.64 tff(141,plain,
% 243.47/155.64 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[140, 121])).
% 243.47/155.64 tff(142,plain,
% 243.47/155.64 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(monotonicity,[status(thm)],[83, 79])).
% 243.47/155.64 tff(143,plain,
% 243.47/155.64 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(symmetry,[status(thm)],[142])).
% 243.47/155.64 tff(144,plain,
% 243.47/155.64 (((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(145,plain,
% 243.47/155.64 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[144, 113])).
% 243.47/155.64 tff(146,plain,
% 243.47/155.64 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[145, 143])).
% 243.47/155.64 tff(147,plain,
% 243.47/155.64 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(monotonicity,[status(thm)],[83])).
% 243.47/155.64 tff(148,plain,
% 243.47/155.64 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(symmetry,[status(thm)],[147])).
% 243.47/155.64 tff(149,plain,
% 243.47/155.64 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))),
% 243.47/155.64 inference(quant_inst,[status(thm)],[])).
% 243.47/155.64 tff(150,plain,
% 243.47/155.64 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[149, 92])).
% 243.47/155.64 tff(151,plain,
% 243.47/155.64 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(monotonicity,[status(thm)],[79])).
% 243.47/155.64 tff(152,plain,
% 243.47/155.64 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(symmetry,[status(thm)],[151])).
% 243.47/155.64 tff(153,plain,
% 243.47/155.64 (((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(154,plain,
% 243.47/155.64 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[153, 138])).
% 243.47/155.64 tff(155,plain,
% 243.47/155.64 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[154, 152])).
% 243.47/155.64 tff(156,plain,
% 243.47/155.64 ((~(m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))) | m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(157,plain,
% 243.47/155.64 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[156, 155, 150])).
% 243.47/155.64 tff(158,plain,
% 243.47/155.64 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[157, 148])).
% 243.47/155.64 tff(159,plain,
% 243.47/155.64 (((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_1(k4_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(160,plain,
% 243.47/155.64 (v1_funct_1(k4_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[159, 138])).
% 243.47/155.64 tff(161,plain,
% 243.47/155.64 (((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_1(k5_lopclset(A!0))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(162,plain,
% 243.47/155.64 (v1_funct_1(k5_lopclset(A!0))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[161, 113])).
% 243.47/155.64 tff(163,plain,
% 243.47/155.64 (^[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)))))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(164,plain,
% 243.47/155.64 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![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))))))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[163])).
% 243.47/155.64 tff(165,plain,
% 243.47/155.64 (^[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))))))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(166,plain,
% 243.47/155.64 (![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))))))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[165])).
% 243.47/155.64 tff(167,plain,
% 243.47/155.64 (![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))))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(168,plain,
% 243.47/155.64 (^[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))))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(169,plain,
% 243.47/155.64 (![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))))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[168])).
% 243.47/155.64 tff(170,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_g3_lattices')).
% 243.47/155.64 tff(171,plain,
% 243.47/155.64 (![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))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[170, 169])).
% 243.47/155.64 tff(172,plain,
% 243.47/155.64 (![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))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[171, 167])).
% 243.47/155.64 tff(173,plain,(
% 243.47/155.64 ![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))))),
% 243.47/155.64 inference(skolemize,[status(sab)],[172])).
% 243.47/155.64 tff(174,plain,
% 243.47/155.64 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[173, 166])).
% 243.47/155.64 tff(175,plain,
% 243.47/155.64 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[174, 164])).
% 243.47/155.64 tff(176,plain,
% 243.47/155.64 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(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(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(177,plain,
% 243.47/155.64 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))))),
% 243.47/155.64 inference(quant_inst,[status(thm)],[])).
% 243.47/155.64 tff(178,plain,
% 243.47/155.64 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[177, 176])).
% 243.47/155.64 tff(179,plain,
% 243.47/155.64 ((~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[178, 175, 162, 160])).
% 243.47/155.64 tff(180,plain,
% 243.47/155.64 (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[179, 158, 146, 141, 119])).
% 243.47/155.64 tff(181,plain,
% 243.47/155.64 (((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))) | v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))),
% 243.47/155.64 inference(tautology,[status(thm)],[])).
% 243.47/155.64 tff(182,plain,
% 243.47/155.64 (v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[181, 180])).
% 243.47/155.64 tff(183,plain,
% 243.47/155.64 (v3_lattices(k6_lopclset(A!0))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[182, 82])).
% 243.47/155.64 tff(184,plain,
% 243.47/155.64 (^[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))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(185,plain,
% 243.47/155.64 (![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)))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[184])).
% 243.47/155.64 tff(186,plain,
% 243.47/155.64 (![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)))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(187,plain,
% 243.47/155.64 (^[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)))))),
% 243.47/155.64 inference(bind,[status(th)],[])).
% 243.47/155.64 tff(188,plain,
% 243.47/155.64 (![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)))),
% 243.47/155.64 inference(quant_intro,[status(thm)],[187])).
% 243.47/155.64 tff(189,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 243.47/155.64 tff(190,plain,
% 243.47/155.64 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[189, 188])).
% 243.47/155.64 tff(191,plain,
% 243.47/155.64 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[190, 186])).
% 243.47/155.64 tff(192,plain,(
% 243.47/155.64 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 243.47/155.64 inference(skolemize,[status(sab)],[191])).
% 243.47/155.64 tff(193,plain,
% 243.47/155.64 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[192, 185])).
% 243.47/155.64 tff(194,plain,
% 243.47/155.64 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))),
% 243.47/155.64 inference(rewrite,[status(thm)],[])).
% 243.47/155.64 tff(195,plain,
% 243.47/155.64 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))),
% 243.47/155.64 inference(quant_inst,[status(thm)],[])).
% 243.47/155.64 tff(196,plain,
% 243.47/155.64 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0)))),
% 243.47/155.64 inference(modus_ponens,[status(thm)],[195, 194])).
% 243.47/155.64 tff(197,plain,
% 243.47/155.64 ((k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0)))),
% 243.47/155.64 inference(unit_resolution,[status(thm)],[196, 193])).
% 243.47/155.64 tff(198,plain,
% 243.47/155.64 (k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[197, 183, 37])).
% 243.47/155.65 tff(199,plain,
% 243.47/155.65 (g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))),
% 243.47/155.65 inference(transitivity,[status(thm)],[80, 58, 198])).
% 243.47/155.65 tff(200,plain,
% 243.47/155.65 (^[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)))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(201,plain,
% 243.47/155.65 (![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))))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[200])).
% 243.47/155.65 tff(202,plain,
% 243.47/155.65 (^[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)))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(203,plain,
% 243.47/155.65 (![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))))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[202])).
% 243.47/155.65 tff(204,plain,
% 243.47/155.65 (![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))))))),
% 243.47/155.65 inference(transitivity,[status(thm)],[203, 201])).
% 243.47/155.65 tff(205,plain,
% 243.47/155.65 (^[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))))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(206,plain,
% 243.47/155.65 (![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))))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[205])).
% 243.47/155.65 tff(207,plain,
% 243.47/155.65 (![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))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(208,plain,
% 243.47/155.65 (^[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))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(209,plain,
% 243.47/155.65 (![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))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[208])).
% 243.47/155.65 tff(210,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 243.47/155.65 tff(211,plain,
% 243.47/155.65 (![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))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[210, 209])).
% 243.47/155.65 tff(212,plain,
% 243.47/155.65 (![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))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[211, 207])).
% 243.47/155.65 tff(213,plain,(
% 243.47/155.65 ![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))))),
% 243.47/155.65 inference(skolemize,[status(sab)],[212])).
% 243.47/155.65 tff(214,plain,
% 243.47/155.65 (![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))))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[213, 206])).
% 243.47/155.65 tff(215,plain,
% 243.47/155.65 (![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))))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[214, 204])).
% 243.47/155.65 tff(216,plain,
% 243.47/155.65 (((~![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(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(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(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F))))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(217,plain,
% 243.47/155.65 ((~![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(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F))))))),
% 243.47/155.65 inference(quant_inst,[status(thm)],[])).
% 243.47/155.65 tff(218,plain,
% 243.47/155.65 ((~![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(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[217, 216])).
% 243.47/155.65 tff(219,plain,
% 243.47/155.65 ((~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[218, 215, 162, 160])).
% 243.47/155.65 tff(220,plain,
% 243.47/155.65 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[219, 158, 146, 141, 119])).
% 243.47/155.65 tff(221,plain,
% 243.47/155.65 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | (~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(222,plain,
% 243.47/155.65 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))))),
% 243.47/155.65 inference(quant_inst,[status(thm)],[])).
% 243.47/155.65 tff(223,plain,
% 243.47/155.65 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | (~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0))))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[222, 221])).
% 243.47/155.65 tff(224,plain,
% 243.47/155.65 (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[223, 220, 199])).
% 243.47/155.65 tff(225,plain,
% 243.47/155.65 (((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0))))) | (a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))),
% 243.47/155.65 inference(tautology,[status(thm)],[])).
% 243.47/155.65 tff(226,plain,
% 243.47/155.65 (a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[225, 224])).
% 243.47/155.65 tff(227,plain,
% 243.47/155.65 (u1_struct_0(k6_lopclset(A!0)) = a_1_0_lopclset(A!0)),
% 243.47/155.65 inference(symmetry,[status(thm)],[226])).
% 243.47/155.65 tff(228,plain,
% 243.47/155.65 (m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 243.47/155.65 inference(monotonicity,[status(thm)],[227])).
% 243.47/155.65 tff(229,plain,
% 243.47/155.65 (m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 243.47/155.65 inference(symmetry,[status(thm)],[228])).
% 243.47/155.65 tff(230,plain,
% 243.47/155.65 (v1_xboole_0(a_1_0_lopclset(A!0)) <=> v1_xboole_0(k1_lopclset(A!0))),
% 243.47/155.65 inference(monotonicity,[status(thm)],[79])).
% 243.47/155.65 tff(231,plain,
% 243.47/155.65 (v1_xboole_0(k1_lopclset(A!0)) <=> v1_xboole_0(a_1_0_lopclset(A!0))),
% 243.47/155.65 inference(symmetry,[status(thm)],[230])).
% 243.47/155.65 tff(232,plain,
% 243.47/155.65 ((~v1_xboole_0(k1_lopclset(A!0))) <=> (~v1_xboole_0(a_1_0_lopclset(A!0)))),
% 243.47/155.65 inference(monotonicity,[status(thm)],[231])).
% 243.47/155.65 tff(233,plain,
% 243.47/155.65 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(234,plain,
% 243.47/155.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[233])).
% 243.47/155.65 tff(235,plain,
% 243.47/155.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> ((~v1_xboole_0(k1_lopclset(A))) | (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))), rewrite(((~v1_xboole_0(k1_lopclset(A))) | (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(236,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[235])).
% 243.47/155.65 tff(237,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> ![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(238,plain,
% 243.47/155.65 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(239,plain,
% 243.47/155.65 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> ![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[238])).
% 243.47/155.65 tff(240,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_lopclset')).
% 243.47/155.65 tff(241,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[240, 239])).
% 243.47/155.65 tff(242,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[241, 237])).
% 243.47/155.65 tff(243,plain,(
% 243.47/155.65 ![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 243.47/155.65 inference(skolemize,[status(sab)],[242])).
% 243.47/155.65 tff(244,plain,
% 243.47/155.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[243, 236])).
% 243.47/155.65 tff(245,plain,
% 243.47/155.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[244, 234])).
% 243.47/155.65 tff(246,plain,
% 243.47/155.65 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(247,plain,
% 243.47/155.65 ((v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(248,plain,
% 243.47/155.65 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0)))))),
% 243.47/155.65 inference(monotonicity,[status(thm)],[247])).
% 243.47/155.65 tff(249,plain,
% 243.47/155.65 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))),
% 243.47/155.65 inference(transitivity,[status(thm)],[248, 246])).
% 243.47/155.65 tff(250,plain,
% 243.47/155.65 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 243.47/155.65 inference(quant_inst,[status(thm)],[])).
% 243.47/155.65 tff(251,plain,
% 243.47/155.65 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[250, 249])).
% 243.47/155.65 tff(252,plain,
% 243.47/155.65 (~v1_xboole_0(k1_lopclset(A!0))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[251, 28, 27, 26, 245])).
% 243.47/155.65 tff(253,plain,
% 243.47/155.65 (~v1_xboole_0(a_1_0_lopclset(A!0))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[252, 232])).
% 243.47/155.65 tff(254,plain,
% 243.47/155.65 (^[A: $i] : refl((~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))) <=> (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(255,plain,
% 243.47/155.65 (![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))) <=> ![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[254])).
% 243.47/155.65 tff(256,plain,
% 243.47/155.65 (^[A: $i] : rewrite(((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A))) <=> (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(257,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A))) <=> ![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[256])).
% 243.47/155.65 tff(258,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A))) <=> ![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(259,plain,
% 243.47/155.65 (^[A: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) <=> ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)))), (((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> (((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))))), rewrite((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))), (((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(260,plain,
% 243.47/155.65 (![A: $i] : ((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> ![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[259])).
% 243.47/155.65 tff(261,axiom,(![A: $i] : ((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_finsub_1')).
% 243.47/155.65 tff(262,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[261, 260])).
% 243.47/155.65 tff(263,plain,
% 243.47/155.65 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[262, 258])).
% 243.47/155.65 tff(264,plain,(
% 243.47/155.65 ![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 243.47/155.65 inference(skolemize,[status(sab)],[263])).
% 243.47/155.65 tff(265,plain,
% 243.47/155.65 (![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[264, 257])).
% 243.47/155.65 tff(266,plain,
% 243.47/155.65 (![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[265, 255])).
% 243.47/155.65 tff(267,plain,
% 243.47/155.65 ((~![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))) | (~(v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | (~v1_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_finsub_1(k1_zfmisc_1(u1_struct_0(A!0))))))),
% 243.47/155.65 inference(quant_inst,[status(thm)],[])).
% 243.47/155.65 tff(268,plain,
% 243.47/155.65 (~(v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | (~v1_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[267, 266])).
% 243.47/155.65 tff(269,plain,
% 243.47/155.65 ((v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | (~v1_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_finsub_1(k1_zfmisc_1(u1_struct_0(A!0))))) | (~v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))))),
% 243.47/155.65 inference(tautology,[status(thm)],[])).
% 243.47/155.65 tff(270,plain,
% 243.47/155.65 (~v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0)))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[269, 268])).
% 243.47/155.65 tff(271,plain,
% 243.47/155.65 (m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) <=> m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 243.47/155.65 inference(monotonicity,[status(thm)],[79])).
% 243.47/155.65 tff(272,plain,
% 243.47/155.65 (m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) <=> m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 243.47/155.65 inference(symmetry,[status(thm)],[271])).
% 243.47/155.65 tff(273,plain,
% 243.47/155.65 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(274,plain,
% 243.47/155.65 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[273])).
% 243.47/155.65 tff(275,plain,
% 243.47/155.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(276,plain,
% 243.47/155.65 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[275])).
% 243.47/155.65 tff(277,plain,
% 243.47/155.65 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(278,plain,
% 243.47/155.65 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.65 tff(279,plain,
% 243.47/155.65 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 243.47/155.65 inference(quant_intro,[status(thm)],[278])).
% 243.47/155.65 tff(280,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lopclset')).
% 243.47/155.65 tff(281,plain,
% 243.47/155.65 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[280, 279])).
% 243.47/155.65 tff(282,plain,
% 243.47/155.65 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[281, 277])).
% 243.47/155.65 tff(283,plain,(
% 243.47/155.65 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 243.47/155.65 inference(skolemize,[status(sab)],[282])).
% 243.47/155.65 tff(284,plain,
% 243.47/155.65 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[283, 276])).
% 243.47/155.65 tff(285,plain,
% 243.47/155.65 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[284, 274])).
% 243.47/155.65 tff(286,plain,
% 243.47/155.65 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(287,plain,
% 243.47/155.65 ((v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 243.47/155.65 inference(rewrite,[status(thm)],[])).
% 243.47/155.65 tff(288,plain,
% 243.47/155.65 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))))),
% 243.47/155.65 inference(monotonicity,[status(thm)],[287])).
% 243.47/155.65 tff(289,plain,
% 243.47/155.65 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 243.47/155.65 inference(transitivity,[status(thm)],[288, 286])).
% 243.47/155.65 tff(290,plain,
% 243.47/155.65 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 243.47/155.65 inference(quant_inst,[status(thm)],[])).
% 243.47/155.65 tff(291,plain,
% 243.47/155.65 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[290, 289])).
% 243.47/155.65 tff(292,plain,
% 243.47/155.65 (m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 243.47/155.65 inference(unit_resolution,[status(thm)],[291, 28, 26, 285])).
% 243.47/155.65 tff(293,plain,
% 243.47/155.65 (m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 243.47/155.65 inference(modus_ponens,[status(thm)],[292, 272])).
% 243.47/155.65 tff(294,plain,
% 243.47/155.65 (^[A: $i, B: $i] : rewrite((v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))))),
% 243.47/155.65 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(295,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[294])).
% 243.47/155.66 tff(296,plain,
% 243.47/155.66 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(297,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[296])).
% 243.47/155.66 tff(298,plain,
% 243.47/155.66 (^[A: $i, B: $i] : rewrite((v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(299,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[298])).
% 243.47/155.66 tff(300,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 243.47/155.66 inference(transitivity,[status(thm)],[299, 297])).
% 243.47/155.66 tff(301,plain,
% 243.47/155.66 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ((v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))))), rewrite(((v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(302,plain,
% 243.47/155.66 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[301])).
% 243.47/155.66 tff(303,plain,
% 243.47/155.66 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(rewrite,[status(thm)],[])).
% 243.47/155.66 tff(304,plain,
% 243.47/155.66 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(305,plain,
% 243.47/155.66 (![A: $i, B: $i] : ((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[304])).
% 243.47/155.66 tff(306,axiom,(![A: $i, B: $i] : ((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_subset_1')).
% 243.47/155.66 tff(307,plain,
% 243.47/155.66 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[306, 305])).
% 243.47/155.66 tff(308,plain,
% 243.47/155.66 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[307, 303])).
% 243.47/155.66 tff(309,plain,(
% 243.47/155.66 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(skolemize,[status(sab)],[308])).
% 243.47/155.66 tff(310,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[309, 302])).
% 243.47/155.66 tff(311,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[310, 300])).
% 243.47/155.66 tff(312,plain,
% 243.47/155.66 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[311, 295])).
% 243.47/155.66 tff(313,plain,
% 243.47/155.66 (((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 243.47/155.66 inference(rewrite,[status(thm)],[])).
% 243.47/155.66 tff(314,plain,
% 243.47/155.66 ((v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))) <=> (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 243.47/155.66 inference(rewrite,[status(thm)],[])).
% 243.47/155.66 tff(315,plain,
% 243.47/155.66 (((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))))),
% 243.47/155.66 inference(monotonicity,[status(thm)],[314])).
% 243.47/155.66 tff(316,plain,
% 243.47/155.66 (((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 243.47/155.66 inference(transitivity,[status(thm)],[315, 313])).
% 243.47/155.66 tff(317,plain,
% 243.47/155.66 ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 243.47/155.66 inference(quant_inst,[status(thm)],[])).
% 243.47/155.66 tff(318,plain,
% 243.47/155.66 ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[317, 316])).
% 243.47/155.66 tff(319,plain,
% 243.47/155.66 (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))),
% 243.47/155.66 inference(unit_resolution,[status(thm)],[318, 312])).
% 243.47/155.66 tff(320,plain,
% 243.47/155.66 (![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))),
% 243.47/155.66 inference(unit_resolution,[status(thm)],[319, 293, 270, 253])).
% 243.47/155.66 tff(321,plain,
% 243.47/155.66 ((~![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))) | (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))),
% 243.47/155.66 inference(quant_inst,[status(thm)],[])).
% 243.47/155.66 tff(322,plain,
% 243.47/155.66 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 243.47/155.66 inference(unit_resolution,[status(thm)],[321, 320])).
% 243.47/155.66 tff(323,plain,
% 243.47/155.66 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0))),
% 243.47/155.66 inference(monotonicity,[status(thm)],[79])).
% 243.47/155.66 tff(324,plain,
% 243.47/155.66 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) <=> m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0))),
% 243.47/155.66 inference(symmetry,[status(thm)],[323])).
% 243.47/155.66 tff(325,plain,
% 243.47/155.66 (^[A: $i] : refl((v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(326,plain,
% 243.47/155.66 (![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[325])).
% 243.47/155.66 tff(327,plain,
% 243.47/155.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(328,plain,
% 243.47/155.66 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[327])).
% 243.47/155.66 tff(329,plain,
% 243.47/155.66 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 243.47/155.66 inference(rewrite,[status(thm)],[])).
% 243.47/155.66 tff(330,plain,
% 243.47/155.66 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))))),
% 243.47/155.66 inference(bind,[status(th)],[])).
% 243.47/155.66 tff(331,plain,
% 243.47/155.66 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 243.47/155.66 inference(quant_intro,[status(thm)],[330])).
% 243.47/155.66 tff(332,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_lopclset')).
% 243.47/155.66 tff(333,plain,
% 243.47/155.66 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[332, 331])).
% 243.47/155.66 tff(334,plain,
% 243.47/155.66 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[333, 329])).
% 243.47/155.66 tff(335,plain,(
% 243.47/155.66 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 243.47/155.66 inference(skolemize,[status(sab)],[334])).
% 243.47/155.66 tff(336,plain,
% 243.47/155.66 (![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[335, 328])).
% 243.47/155.66 tff(337,plain,
% 243.47/155.66 (![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 243.47/155.66 inference(modus_ponens,[status(thm)],[336, 326])).
% 243.47/155.66 tff(338,plain,
% 243.47/155.66 (((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 243.47/155.66 inference(rewrite,[status(thm)],[])).
% 243.47/155.66 tff(339,plain,
% 243.47/155.66 ((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 243.47/155.66 inference(quant_inst,[status(thm)],[])).
% 243.47/155.66 tff(340,plain,
% 243.47/155.66 ((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))),
% 244.23/156.34 inference(modus_ponens,[status(thm)],[339, 338])).
% 244.23/156.34 tff(341,plain,
% 244.23/156.34 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0))),
% 244.23/156.34 inference(unit_resolution,[status(thm)],[340, 28, 27, 26, 337])).
% 244.23/156.34 tff(342,plain,
% 244.23/156.34 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0))),
% 244.23/156.34 inference(modus_ponens,[status(thm)],[341, 324])).
% 244.23/156.34 tff(343,plain,
% 244.23/156.34 ((~(m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))) | (~m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0))) | m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 244.23/156.34 inference(tautology,[status(thm)],[])).
% 244.23/156.34 tff(344,plain,
% 244.23/156.34 (m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 244.23/156.34 inference(unit_resolution,[status(thm)],[343, 342, 322])).
% 244.23/156.34 tff(345,plain,
% 244.23/156.34 (m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 244.23/156.34 inference(modus_ponens,[status(thm)],[344, 229])).
% 244.23/156.34 tff(346,plain,
% 244.23/156.34 (~m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 244.23/156.34 inference(or_elim,[status(thm)],[24])).
% 244.23/156.34 tff(347,plain,
% 244.23/156.34 ($false),
% 244.23/156.34 inference(unit_resolution,[status(thm)],[346, 345])).
% 244.23/156.34 % SZS output end Proof
%------------------------------------------------------------------------------