TSTP Solution File: LAT319+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT319+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 18:33:02 EDT 2022
% Result : Theorem 57.07s 36.82s
% Output : Proof 57.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT319+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 13:43:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 57.07/36.82 % SZS status Theorem
% 57.07/36.82 % SZS output start Proof
% 57.07/36.82 tff(v15_lattices_type, type, (
% 57.07/36.82 v15_lattices: $i > $o)).
% 57.07/36.82 tff(g3_lattices_type, type, (
% 57.07/36.82 g3_lattices: ( $i * $i * $i ) > $i)).
% 57.07/36.82 tff(u2_lattices_type, type, (
% 57.07/36.82 u2_lattices: $i > $i)).
% 57.07/36.82 tff(tptp_fun_A_0_type, type, (
% 57.07/36.82 tptp_fun_A_0: $i)).
% 57.07/36.82 tff(u1_lattices_type, type, (
% 57.07/36.82 u1_lattices: $i > $i)).
% 57.07/36.82 tff(u1_struct_0_type, type, (
% 57.07/36.82 u1_struct_0: $i > $i)).
% 57.07/36.82 tff(k1_lattice2_type, type, (
% 57.07/36.82 k1_lattice2: $i > $i)).
% 57.07/36.82 tff(l3_lattices_type, type, (
% 57.07/36.82 l3_lattices: $i > $o)).
% 57.07/36.82 tff(v10_lattices_type, type, (
% 57.07/36.82 v10_lattices: $i > $o)).
% 57.07/36.82 tff(v3_struct_0_type, type, (
% 57.07/36.82 v3_struct_0: $i > $o)).
% 57.07/36.82 tff(v17_lattices_type, type, (
% 57.07/36.82 v17_lattices: $i > $o)).
% 57.07/36.82 tff(v16_lattices_type, type, (
% 57.07/36.82 v16_lattices: $i > $o)).
% 57.07/36.82 tff(v11_lattices_type, type, (
% 57.07/36.82 v11_lattices: $i > $o)).
% 57.07/36.82 tff(v9_lattices_type, type, (
% 57.07/36.82 v9_lattices: $i > $o)).
% 57.07/36.82 tff(v8_lattices_type, type, (
% 57.07/36.82 v8_lattices: $i > $o)).
% 57.07/36.82 tff(v7_lattices_type, type, (
% 57.07/36.82 v7_lattices: $i > $o)).
% 57.07/36.82 tff(v6_lattices_type, type, (
% 57.07/36.82 v6_lattices: $i > $o)).
% 57.07/36.82 tff(v5_lattices_type, type, (
% 57.07/36.82 v5_lattices: $i > $o)).
% 57.07/36.82 tff(v4_lattices_type, type, (
% 57.07/36.82 v4_lattices: $i > $o)).
% 57.07/36.82 tff(v3_lattices_type, type, (
% 57.07/36.82 v3_lattices: $i > $o)).
% 57.07/36.82 tff(1,plain,
% 57.07/36.82 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(2,plain,
% 57.07/36.82 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[1])).
% 57.07/36.82 tff(3,plain,
% 57.07/36.82 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(4,plain,
% 57.07/36.82 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(5,plain,
% 57.07/36.82 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[4])).
% 57.07/36.82 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 57.07/36.82 tff(7,plain,
% 57.07/36.82 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[6, 5])).
% 57.07/36.82 tff(8,plain,
% 57.07/36.82 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[7, 3])).
% 57.07/36.82 tff(9,plain,(
% 57.07/36.82 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(skolemize,[status(sab)],[8])).
% 57.07/36.82 tff(10,plain,
% 57.07/36.82 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[9, 2])).
% 57.07/36.82 tff(11,plain,
% 57.07/36.82 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(12,plain,
% 57.07/36.82 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(13,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t54_filter_2')).
% 57.07/36.82 tff(14,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[13, 12])).
% 57.07/36.82 tff(15,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[14, 11])).
% 57.07/36.82 tff(16,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[15, 11])).
% 57.07/36.82 tff(17,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[16, 11])).
% 57.07/36.82 tff(18,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[17, 11])).
% 57.07/36.82 tff(19,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[18, 11])).
% 57.07/36.82 tff(20,plain,
% 57.07/36.82 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[19, 11])).
% 57.07/36.82 tff(21,plain,(
% 57.07/36.82 ~((~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))) | (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> ((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.82 inference(skolemize,[status(sab)],[20])).
% 57.07/36.82 tff(22,plain,
% 57.07/36.82 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 57.07/36.82 inference(or_elim,[status(thm)],[21])).
% 57.07/36.82 tff(23,plain,
% 57.07/36.82 (l3_lattices(A!0)),
% 57.07/36.82 inference(and_elim,[status(thm)],[22])).
% 57.07/36.82 tff(24,plain,
% 57.07/36.82 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(25,plain,
% 57.07/36.82 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 57.07/36.82 inference(quant_inst,[status(thm)],[])).
% 57.07/36.82 tff(26,plain,
% 57.07/36.82 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[25, 24])).
% 57.07/36.82 tff(27,plain,
% 57.07/36.82 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 57.07/36.82 tff(28,plain,
% 57.07/36.82 (v15_lattices(k1_lattice2(A!0)) <=> v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[27])).
% 57.07/36.82 tff(29,assumption,(~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))), introduced(assumption)).
% 57.07/36.82 tff(30,plain,
% 57.07/36.82 ((~((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))) <=> ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(31,plain,
% 57.07/36.82 (((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))) <=> ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(32,plain,
% 57.07/36.82 (((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0))) <=> (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(33,plain,
% 57.07/36.82 (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(34,plain,
% 57.07/36.82 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> ((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0)))) <=> ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[33, 32])).
% 57.07/36.82 tff(35,plain,
% 57.07/36.82 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> ((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0)))) <=> ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.82 inference(transitivity,[status(thm)],[34, 31])).
% 57.07/36.82 tff(36,plain,
% 57.07/36.82 ((~(((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> ((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0))))) <=> (~((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[35])).
% 57.07/36.82 tff(37,plain,
% 57.07/36.82 ((~(((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> ((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0))))) <=> ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.82 inference(transitivity,[status(thm)],[36, 30])).
% 57.07/36.82 tff(38,plain,
% 57.07/36.82 (~(((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) <=> ((~v3_struct_0(k1_lattice2(A!0))) & v10_lattices(k1_lattice2(A!0)) & v17_lattices(k1_lattice2(A!0)) & l3_lattices(k1_lattice2(A!0))))),
% 57.07/36.82 inference(or_elim,[status(thm)],[21])).
% 57.07/36.82 tff(39,plain,
% 57.07/36.82 ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[38, 37])).
% 57.07/36.82 tff(40,plain,
% 57.07/36.82 ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) | (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))) | (~((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.82 inference(tautology,[status(thm)],[])).
% 57.07/36.82 tff(41,plain,
% 57.07/36.82 ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) | (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[40, 39])).
% 57.07/36.82 tff(42,plain,
% 57.07/36.82 (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[41, 29])).
% 57.07/36.82 tff(43,plain,
% 57.07/36.82 (v10_lattices(A!0)),
% 57.07/36.82 inference(and_elim,[status(thm)],[22])).
% 57.07/36.82 tff(44,plain,
% 57.07/36.82 (~v3_struct_0(A!0)),
% 57.07/36.82 inference(and_elim,[status(thm)],[22])).
% 57.07/36.82 tff(45,plain,
% 57.07/36.82 ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))),
% 57.07/36.82 inference(tautology,[status(thm)],[])).
% 57.07/36.82 tff(46,plain,
% 57.07/36.82 ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) | (~v17_lattices(A!0))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[45, 44, 43, 23])).
% 57.07/36.82 tff(47,plain,
% 57.07/36.82 (~v17_lattices(A!0)),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[46, 42])).
% 57.07/36.82 tff(48,plain,
% 57.07/36.82 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)))))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(49,plain,
% 57.07/36.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[48])).
% 57.07/36.82 tff(50,plain,
% 57.07/36.82 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A))))), rewrite((v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))) <=> (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A))) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A))) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(51,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[50])).
% 57.07/36.82 tff(52,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(53,plain,
% 57.07/36.82 (^[A: $i] : trans(monotonicity(rewrite((v17_lattices(A) <=> ((v15_lattices(A) & v16_lattices(A)) & v11_lattices(A))) <=> (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))), ((((~v3_struct_0(A)) & l3_lattices(A)) => (v17_lattices(A) <=> ((v15_lattices(A) & v16_lattices(A)) & v11_lattices(A)))) <=> (((~v3_struct_0(A)) & l3_lattices(A)) => (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))))), rewrite((((~v3_struct_0(A)) & l3_lattices(A)) => (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A)))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => (v17_lattices(A) <=> ((v15_lattices(A) & v16_lattices(A)) & v11_lattices(A)))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(54,plain,
% 57.07/36.82 (![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => (v17_lattices(A) <=> ((v15_lattices(A) & v16_lattices(A)) & v11_lattices(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[53])).
% 57.07/36.82 tff(55,axiom,(![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => (v17_lattices(A) <=> ((v15_lattices(A) & v16_lattices(A)) & v11_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d20_lattices')).
% 57.07/36.82 tff(56,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[55, 54])).
% 57.07/36.82 tff(57,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[56, 52])).
% 57.07/36.82 tff(58,plain,(
% 57.07/36.82 ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 57.07/36.82 inference(skolemize,[status(sab)],[57])).
% 57.07/36.82 tff(59,plain,
% 57.07/36.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[58, 51])).
% 57.07/36.82 tff(60,plain,
% 57.07/36.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[59, 49])).
% 57.07/36.82 tff(61,plain,
% 57.07/36.82 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(62,plain,
% 57.07/36.82 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))))))),
% 57.07/36.82 inference(quant_inst,[status(thm)],[])).
% 57.07/36.82 tff(63,plain,
% 57.07/36.82 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[62, 61])).
% 57.07/36.82 tff(64,plain,
% 57.07/36.82 (v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[63, 44, 23, 60])).
% 57.07/36.82 tff(65,plain,
% 57.07/36.82 ((~(v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))))) | v17_lattices(A!0) | ((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))),
% 57.07/36.82 inference(tautology,[status(thm)],[])).
% 57.07/36.82 tff(66,plain,
% 57.07/36.82 (v17_lattices(A!0) | ((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[65, 64])).
% 57.07/36.82 tff(67,plain,
% 57.07/36.82 ((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[66, 47])).
% 57.07/36.82 tff(68,plain,
% 57.07/36.82 (v16_lattices(k1_lattice2(A!0)) <=> v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[27])).
% 57.07/36.82 tff(69,plain,
% 57.07/36.82 (v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v16_lattices(k1_lattice2(A!0))),
% 57.07/36.82 inference(symmetry,[status(thm)],[68])).
% 57.07/36.82 tff(70,plain,
% 57.07/36.82 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 57.07/36.82 inference(symmetry,[status(thm)],[27])).
% 57.07/36.82 tff(71,plain,
% 57.07/36.82 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v17_lattices(k1_lattice2(A!0))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[70])).
% 57.07/36.82 tff(72,plain,
% 57.07/36.82 (v17_lattices(k1_lattice2(A!0)) <=> v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.82 inference(symmetry,[status(thm)],[71])).
% 57.07/36.82 tff(73,plain,
% 57.07/36.82 ((v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))) | v17_lattices(k1_lattice2(A!0))),
% 57.07/36.82 inference(tautology,[status(thm)],[])).
% 57.07/36.82 tff(74,plain,
% 57.07/36.82 (v17_lattices(k1_lattice2(A!0))),
% 57.07/36.82 inference(unit_resolution,[status(thm)],[73, 29])).
% 57.07/36.82 tff(75,plain,
% 57.07/36.82 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[74, 72])).
% 57.07/36.82 tff(76,plain,
% 57.07/36.82 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[70])).
% 57.07/36.82 tff(77,plain,
% 57.07/36.82 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.82 inference(symmetry,[status(thm)],[76])).
% 57.07/36.82 tff(78,plain,
% 57.07/36.82 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 57.07/36.82 inference(monotonicity,[status(thm)],[77])).
% 57.07/36.82 tff(79,plain,
% 57.07/36.82 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(80,plain,
% 57.07/36.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[79])).
% 57.07/36.82 tff(81,plain,
% 57.07/36.82 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(82,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[81])).
% 57.07/36.82 tff(83,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 57.07/36.82 inference(rewrite,[status(thm)],[])).
% 57.07/36.82 tff(84,plain,
% 57.07/36.82 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 57.07/36.82 inference(bind,[status(th)],[])).
% 57.07/36.82 tff(85,plain,
% 57.07/36.82 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 57.07/36.82 inference(quant_intro,[status(thm)],[84])).
% 57.07/36.82 tff(86,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 57.07/36.82 tff(87,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[86, 85])).
% 57.07/36.82 tff(88,plain,
% 57.07/36.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[87, 83])).
% 57.07/36.82 tff(89,plain,(
% 57.07/36.82 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 57.07/36.82 inference(skolemize,[status(sab)],[88])).
% 57.07/36.82 tff(90,plain,
% 57.07/36.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 57.07/36.82 inference(modus_ponens,[status(thm)],[89, 82])).
% 57.07/36.82 tff(91,plain,
% 57.07/36.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[90, 80])).
% 57.07/36.83 tff(92,plain,
% 57.07/36.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(93,plain,
% 57.07/36.83 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(94,plain,
% 57.07/36.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0)))))))),
% 57.07/36.83 inference(monotonicity,[status(thm)],[93])).
% 57.07/36.83 tff(95,plain,
% 57.07/36.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(transitivity,[status(thm)],[94, 92])).
% 57.07/36.83 tff(96,plain,
% 57.07/36.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(quant_inst,[status(thm)],[])).
% 57.07/36.83 tff(97,plain,
% 57.07/36.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0)))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[96, 95])).
% 57.07/36.83 tff(98,plain,
% 57.07/36.83 (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[97, 44, 43, 23, 91])).
% 57.07/36.83 tff(99,plain,
% 57.07/36.83 ((v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(100,plain,
% 57.07/36.83 (~v3_struct_0(k1_lattice2(A!0))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[99, 98])).
% 57.07/36.83 tff(101,plain,
% 57.07/36.83 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[100, 78])).
% 57.07/36.83 tff(102,plain,
% 57.07/36.83 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> l3_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(monotonicity,[status(thm)],[70])).
% 57.07/36.83 tff(103,plain,
% 57.07/36.83 (l3_lattices(k1_lattice2(A!0)) <=> l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(symmetry,[status(thm)],[102])).
% 57.07/36.83 tff(104,plain,
% 57.07/36.83 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A)))))) <=> ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A)))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(105,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A)))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[104])).
% 57.07/36.83 tff(106,plain,
% 57.07/36.83 (^[A: $i] : rewrite(((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A)))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(107,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[106])).
% 57.07/36.83 tff(108,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(109,plain,
% 57.07/36.83 (^[A: $i] : rewrite((l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(110,plain,
% 57.07/36.83 (![A: $i] : (l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[109])).
% 57.07/36.83 tff(111,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lattice2')).
% 57.07/36.83 tff(112,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[111, 110])).
% 57.07/36.83 tff(113,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[112, 108])).
% 57.07/36.83 tff(114,plain,(
% 57.07/36.83 ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 57.07/36.83 inference(skolemize,[status(sab)],[113])).
% 57.07/36.83 tff(115,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[114, 107])).
% 57.07/36.83 tff(116,plain,
% 57.07/36.83 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[115, 105])).
% 57.07/36.83 tff(117,plain,
% 57.07/36.83 (((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | ((~l3_lattices(A!0)) | (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | (~l3_lattices(A!0)) | (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(118,plain,
% 57.07/36.83 (((~l3_lattices(A!0)) | (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))) <=> ((~l3_lattices(A!0)) | (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(119,plain,
% 57.07/36.83 (((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | ((~l3_lattices(A!0)) | (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | ((~l3_lattices(A!0)) | (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0)))))))),
% 57.07/36.83 inference(monotonicity,[status(thm)],[118])).
% 57.07/36.83 tff(120,plain,
% 57.07/36.83 (((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | ((~l3_lattices(A!0)) | (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | (~l3_lattices(A!0)) | (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(transitivity,[status(thm)],[119, 117])).
% 57.07/36.83 tff(121,plain,
% 57.07/36.83 ((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | ((~l3_lattices(A!0)) | (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(quant_inst,[status(thm)],[])).
% 57.07/36.83 tff(122,plain,
% 57.07/36.83 ((~![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))) | (~l3_lattices(A!0)) | (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[121, 120])).
% 57.07/36.83 tff(123,plain,
% 57.07/36.83 (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[122, 23, 116])).
% 57.07/36.83 tff(124,plain,
% 57.07/36.83 (((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0)))) | l3_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(125,plain,
% 57.07/36.83 (l3_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[124, 123])).
% 57.07/36.83 tff(126,plain,
% 57.07/36.83 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[125, 103])).
% 57.07/36.83 tff(127,plain,
% 57.07/36.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(128,plain,
% 57.07/36.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 57.07/36.83 inference(quant_inst,[status(thm)],[])).
% 57.07/36.83 tff(129,plain,
% 57.07/36.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[128, 127])).
% 57.07/36.83 tff(130,plain,
% 57.07/36.83 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[129, 60])).
% 57.07/36.83 tff(131,plain,
% 57.07/36.83 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[130, 126, 101])).
% 57.07/36.83 tff(132,plain,
% 57.07/36.83 ((~(v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(133,plain,
% 57.07/36.83 ((~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[132, 131])).
% 57.07/36.83 tff(134,plain,
% 57.07/36.83 (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[133, 75])).
% 57.07/36.83 tff(135,plain,
% 57.07/36.83 (((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(136,plain,
% 57.07/36.83 (v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[135, 134])).
% 57.07/36.83 tff(137,plain,
% 57.07/36.83 (v16_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[136, 69])).
% 57.07/36.83 tff(138,plain,
% 57.07/36.83 (v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v15_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(symmetry,[status(thm)],[28])).
% 57.07/36.83 tff(139,plain,
% 57.07/36.83 (((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(140,plain,
% 57.07/36.83 (v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[139, 134])).
% 57.07/36.83 tff(141,plain,
% 57.07/36.83 (v15_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[140, 138])).
% 57.07/36.83 tff(142,plain,
% 57.07/36.83 ((v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(143,plain,
% 57.07/36.83 (v10_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[142, 98])).
% 57.07/36.83 tff(144,plain,
% 57.07/36.83 ((~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))) | v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(145,plain,
% 57.07/36.83 ((~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))) | (~l3_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[144, 100, 143])).
% 57.07/36.83 tff(146,plain,
% 57.07/36.83 ((~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[145, 125])).
% 57.07/36.83 tff(147,plain,
% 57.07/36.83 (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[146, 141, 137])).
% 57.07/36.83 tff(148,plain,
% 57.07/36.83 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(149,plain,
% 57.07/36.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[148])).
% 57.07/36.83 tff(150,plain,
% 57.07/36.83 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))), ((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ((~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))))), rewrite(((~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))), ((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(151,plain,
% 57.07/36.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[150])).
% 57.07/36.83 tff(152,plain,
% 57.07/36.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(153,plain,
% 57.07/36.83 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), rewrite(((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(154,plain,
% 57.07/36.83 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[153])).
% 57.07/36.83 tff(155,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t53_filter_2')).
% 57.07/36.83 tff(156,plain,
% 57.07/36.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[155, 154])).
% 57.07/36.83 tff(157,plain,
% 57.07/36.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[156, 152])).
% 57.07/36.83 tff(158,plain,(
% 57.07/36.83 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(skolemize,[status(sab)],[157])).
% 57.07/36.83 tff(159,plain,
% 57.07/36.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[158, 151])).
% 57.07/36.83 tff(160,plain,
% 57.07/36.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[159, 149])).
% 57.07/36.83 tff(161,plain,
% 57.07/36.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(162,plain,
% 57.07/36.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))))),
% 57.07/36.83 inference(quant_inst,[status(thm)],[])).
% 57.07/36.83 tff(163,plain,
% 57.07/36.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[162, 161])).
% 57.07/36.83 tff(164,plain,
% 57.07/36.83 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[163, 44, 43, 23, 160])).
% 57.07/36.83 tff(165,plain,
% 57.07/36.83 ((~((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))))) | (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(166,plain,
% 57.07/36.83 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[165, 164])).
% 57.07/36.83 tff(167,plain,
% 57.07/36.83 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[166, 147])).
% 57.07/36.83 tff(168,plain,
% 57.07/36.83 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v16_lattices(A!0)),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(169,plain,
% 57.07/36.83 (v16_lattices(A!0)),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[168, 167])).
% 57.07/36.83 tff(170,plain,
% 57.07/36.83 (v11_lattices(k1_lattice2(A!0)) <=> v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(monotonicity,[status(thm)],[27])).
% 57.07/36.83 tff(171,plain,
% 57.07/36.83 (v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v11_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(symmetry,[status(thm)],[170])).
% 57.07/36.83 tff(172,plain,
% 57.07/36.83 (((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(173,plain,
% 57.07/36.83 (v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[172, 134])).
% 57.07/36.83 tff(174,plain,
% 57.07/36.83 (v11_lattices(k1_lattice2(A!0))),
% 57.07/36.83 inference(modus_ponens,[status(thm)],[173, 171])).
% 57.07/36.83 tff(175,plain,
% 57.07/36.83 ((~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))) | v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))),
% 57.07/36.83 inference(tautology,[status(thm)],[])).
% 57.07/36.83 tff(176,plain,
% 57.07/36.83 ((~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))) | (~l3_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[175, 100, 143])).
% 57.07/36.83 tff(177,plain,
% 57.07/36.83 ((~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))) | (~v11_lattices(k1_lattice2(A!0)))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[176, 125])).
% 57.07/36.83 tff(178,plain,
% 57.07/36.83 (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))),
% 57.07/36.83 inference(unit_resolution,[status(thm)],[177, 174])).
% 57.07/36.83 tff(179,plain,
% 57.07/36.83 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(180,plain,
% 57.07/36.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[179])).
% 57.07/36.83 tff(181,plain,
% 57.07/36.83 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))), ((((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ((~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))))), rewrite(((~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))), ((((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(182,plain,
% 57.07/36.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))),
% 57.07/36.83 inference(quant_intro,[status(thm)],[181])).
% 57.07/36.83 tff(183,plain,
% 57.07/36.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.83 inference(rewrite,[status(thm)],[])).
% 57.07/36.83 tff(184,plain,
% 57.07/36.83 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), rewrite((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))))),
% 57.07/36.83 inference(bind,[status(th)],[])).
% 57.07/36.83 tff(185,plain,
% 57.07/36.83 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.84 inference(quant_intro,[status(thm)],[184])).
% 57.07/36.84 tff(186,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & l3_lattices(A)) <=> ((((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & l3_lattices(k1_lattice2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t65_lattice2')).
% 57.07/36.84 tff(187,plain,
% 57.07/36.84 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[186, 185])).
% 57.07/36.84 tff(188,plain,
% 57.07/36.84 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[187, 183])).
% 57.07/36.84 tff(189,plain,(
% 57.07/36.84 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A)) <=> ((~v3_struct_0(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)))))),
% 57.07/36.84 inference(skolemize,[status(sab)],[188])).
% 57.07/36.84 tff(190,plain,
% 57.07/36.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[189, 182])).
% 57.07/36.84 tff(191,plain,
% 57.07/36.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[190, 180])).
% 57.07/36.84 tff(192,plain,
% 57.07/36.84 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))))),
% 57.07/36.84 inference(rewrite,[status(thm)],[])).
% 57.07/36.84 tff(193,plain,
% 57.07/36.84 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))))),
% 57.07/36.84 inference(quant_inst,[status(thm)],[])).
% 57.07/36.84 tff(194,plain,
% 57.07/36.84 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A))) <=> (v3_struct_0(k1_lattice2(A)) | (~l3_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[193, 192])).
% 57.07/36.84 tff(195,plain,
% 57.07/36.84 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[194, 44, 43, 23, 191])).
% 57.07/36.84 tff(196,plain,
% 57.07/36.84 ((~((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))))) | (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))) | (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(197,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))) | (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[196, 195])).
% 57.07/36.84 tff(198,plain,
% 57.07/36.84 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[197, 178])).
% 57.07/36.84 tff(199,plain,
% 57.07/36.84 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) | v11_lattices(A!0)),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(200,plain,
% 57.07/36.84 (v11_lattices(A!0)),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[199, 198])).
% 57.07/36.84 tff(201,plain,
% 57.07/36.84 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v15_lattices(A!0)),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(202,plain,
% 57.07/36.84 (v15_lattices(A!0)),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[201, 167])).
% 57.07/36.84 tff(203,plain,
% 57.07/36.84 ((~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(204,plain,
% 57.07/36.84 ($false),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[203, 202, 200, 169, 67])).
% 57.07/36.84 tff(205,plain,(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))), inference(lemma,lemma(discharge,[]))).
% 57.07/36.84 tff(206,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))) | (~((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(207,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[206, 39])).
% 57.07/36.84 tff(208,plain,
% 57.07/36.84 (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[207, 205])).
% 57.07/36.84 tff(209,plain,
% 57.07/36.84 ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) | v17_lattices(A!0)),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(210,plain,
% 57.07/36.84 (v17_lattices(A!0)),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[209, 208])).
% 57.07/36.84 tff(211,plain,
% 57.07/36.84 ((~(v17_lattices(A!0) <=> (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))))) | (~v17_lattices(A!0)) | (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(212,plain,
% 57.07/36.84 ((~v17_lattices(A!0)) | (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[211, 64])).
% 57.07/36.84 tff(213,plain,
% 57.07/36.84 (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[212, 210])).
% 57.07/36.84 tff(214,plain,
% 57.07/36.84 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v15_lattices(A!0)),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(215,plain,
% 57.07/36.84 (v15_lattices(A!0)),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[214, 213])).
% 57.07/36.84 tff(216,plain,
% 57.07/36.84 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v16_lattices(A!0)),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(217,plain,
% 57.07/36.84 (v16_lattices(A!0)),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[216, 213])).
% 57.07/36.84 tff(218,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(219,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[218, 44, 43, 23])).
% 57.07/36.84 tff(220,plain,
% 57.07/36.84 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[219, 217, 215])).
% 57.07/36.84 tff(221,plain,
% 57.07/36.84 ((~((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(222,plain,
% 57.07/36.84 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[221, 164])).
% 57.07/36.84 tff(223,plain,
% 57.07/36.84 (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[222, 220])).
% 57.07/36.84 tff(224,plain,
% 57.07/36.84 ((v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))) | v15_lattices(k1_lattice2(A!0))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(225,plain,
% 57.07/36.84 (v15_lattices(k1_lattice2(A!0))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[224, 223])).
% 57.07/36.84 tff(226,plain,
% 57.07/36.84 (v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[225, 28])).
% 57.07/36.84 tff(227,plain,
% 57.07/36.84 ((v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0)))) | v16_lattices(k1_lattice2(A!0))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(228,plain,
% 57.07/36.84 (v16_lattices(k1_lattice2(A!0))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[227, 223])).
% 57.07/36.84 tff(229,plain,
% 57.07/36.84 (v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[228, 68])).
% 57.07/36.84 tff(230,plain,
% 57.07/36.84 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v11_lattices(A!0)),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(231,plain,
% 57.07/36.84 (v11_lattices(A!0)),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[230, 213])).
% 57.07/36.84 tff(232,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(233,plain,
% 57.07/36.84 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))) | (~v11_lattices(A!0))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[232, 44, 43, 23])).
% 57.07/36.84 tff(234,plain,
% 57.07/36.84 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[233, 231])).
% 57.07/36.84 tff(235,plain,
% 57.07/36.84 ((~((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) <=> (v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) | (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(236,plain,
% 57.07/36.84 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) | (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[235, 195])).
% 57.07/36.84 tff(237,plain,
% 57.07/36.84 (~(v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[236, 234])).
% 57.07/36.84 tff(238,plain,
% 57.07/36.84 ((v3_struct_0(k1_lattice2(A!0)) | (~l3_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0)))) | v11_lattices(k1_lattice2(A!0))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(239,plain,
% 57.07/36.84 (v11_lattices(k1_lattice2(A!0))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[238, 237])).
% 57.07/36.84 tff(240,plain,
% 57.07/36.84 (v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.07/36.84 inference(modus_ponens,[status(thm)],[239, 170])).
% 57.07/36.84 tff(241,plain,
% 57.07/36.84 ((~v17_lattices(k1_lattice2(A!0))) <=> (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 57.07/36.84 inference(monotonicity,[status(thm)],[72])).
% 57.07/36.84 tff(242,plain,
% 57.07/36.84 ((~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))) | v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))),
% 57.07/36.84 inference(tautology,[status(thm)],[])).
% 57.07/36.84 tff(243,plain,
% 57.07/36.84 ((~(v3_struct_0(k1_lattice2(A!0)) | (~v10_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))) | (~v17_lattices(k1_lattice2(A!0)))),
% 57.07/36.84 inference(unit_resolution,[status(thm)],[242, 100, 143, 125])).
% 57.07/36.84 tff(244,plain,
% 57.07/36.84 (~v17_lattices(k1_lattice2(A!0))),
% 57.16/36.97 inference(unit_resolution,[status(thm)],[243, 205])).
% 57.16/36.97 tff(245,plain,
% 57.16/36.97 (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 57.16/36.97 inference(modus_ponens,[status(thm)],[244, 241])).
% 57.16/36.97 tff(246,plain,
% 57.16/36.97 ((~(v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> (~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | ((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 57.16/36.97 inference(tautology,[status(thm)],[])).
% 57.16/36.97 tff(247,plain,
% 57.16/36.97 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | ((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 57.16/36.97 inference(unit_resolution,[status(thm)],[246, 131])).
% 57.16/36.97 tff(248,plain,
% 57.16/36.97 ((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 57.16/36.97 inference(unit_resolution,[status(thm)],[247, 245])).
% 57.16/36.97 tff(249,plain,
% 57.16/36.97 ((~((~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 57.16/36.97 inference(tautology,[status(thm)],[])).
% 57.16/36.97 tff(250,plain,
% 57.16/36.97 ($false),
% 57.16/36.97 inference(unit_resolution,[status(thm)],[249, 248, 240, 229, 226])).
% 57.16/36.97 % SZS output end Proof
%------------------------------------------------------------------------------