%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT319+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:20 AM UTC 2025
% Result : Theorem 38.15s 38.35s
% Output : Proof 38.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT319+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 20:16:11 EDT 2025
% 0.13/0.35 % CPUTime :
% 38.15/38.35 % SZS status Theorem
% 38.15/38.35 % SZS output start Proof
% 38.15/38.35 tff(v17_lattices_type, type, (
% 38.15/38.35 v17_lattices: $i > $o)).
% 38.15/38.35 tff(g3_lattices_type, type, (
% 38.15/38.35 g3_lattices: ( $i * $i * $i ) > $i)).
% 38.15/38.35 tff(u2_lattices_type, type, (
% 38.15/38.35 u2_lattices: $i > $i)).
% 38.15/38.35 tff(tptp_fun_A_0_type, type, (
% 38.15/38.35 tptp_fun_A_0: $i)).
% 38.15/38.35 tff(u1_lattices_type, type, (
% 38.15/38.35 u1_lattices: $i > $i)).
% 38.15/38.35 tff(u1_struct_0_type, type, (
% 38.15/38.35 u1_struct_0: $i > $i)).
% 38.15/38.35 tff(k1_lattice2_type, type, (
% 38.15/38.35 k1_lattice2: $i > $i)).
% 38.15/38.35 tff(l3_lattices_type, type, (
% 38.15/38.35 l3_lattices: $i > $o)).
% 38.15/38.35 tff(v10_lattices_type, type, (
% 38.15/38.35 v10_lattices: $i > $o)).
% 38.15/38.35 tff(v3_struct_0_type, type, (
% 38.15/38.35 v3_struct_0: $i > $o)).
% 38.15/38.35 tff(v16_lattices_type, type, (
% 38.15/38.35 v16_lattices: $i > $o)).
% 38.15/38.35 tff(v11_lattices_type, type, (
% 38.15/38.35 v11_lattices: $i > $o)).
% 38.15/38.35 tff(v15_lattices_type, type, (
% 38.15/38.35 v15_lattices: $i > $o)).
% 38.15/38.35 tff(v9_lattices_type, type, (
% 38.15/38.35 v9_lattices: $i > $o)).
% 38.15/38.35 tff(v8_lattices_type, type, (
% 38.15/38.35 v8_lattices: $i > $o)).
% 38.15/38.35 tff(v7_lattices_type, type, (
% 38.15/38.35 v7_lattices: $i > $o)).
% 38.15/38.35 tff(v6_lattices_type, type, (
% 38.15/38.35 v6_lattices: $i > $o)).
% 38.15/38.35 tff(v5_lattices_type, type, (
% 38.15/38.35 v5_lattices: $i > $o)).
% 38.15/38.35 tff(v4_lattices_type, type, (
% 38.15/38.35 v4_lattices: $i > $o)).
% 38.15/38.35 tff(v3_lattices_type, type, (
% 38.15/38.35 v3_lattices: $i > $o)).
% 38.15/38.35 tff(1,plain,
% 38.15/38.35 (^[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)))))),
% 38.15/38.35 inference(bind,[status(th)],[])).
% 38.15/38.35 tff(2,plain,
% 38.15/38.35 (![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))))),
% 38.15/38.35 inference(quant_intro,[status(thm)],[1])).
% 38.15/38.35 tff(3,plain,
% 38.15/38.35 (![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))))),
% 38.15/38.35 inference(rewrite,[status(thm)],[])).
% 38.15/38.35 tff(4,plain,
% 38.15/38.35 (^[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)))))),
% 38.15/38.35 inference(bind,[status(th)],[])).
% 38.15/38.35 tff(5,plain,
% 38.15/38.35 (![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))))),
% 38.15/38.35 inference(quant_intro,[status(thm)],[4])).
% 38.15/38.35 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 38.15/38.35 tff(7,plain,
% 38.15/38.35 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[6, 5])).
% 38.15/38.35 tff(8,plain,
% 38.15/38.35 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 38.15/38.35 tff(9,plain,(
% 38.15/38.35 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 38.15/38.35 inference(skolemize,[status(sab)],[8])).
% 38.15/38.35 tff(10,plain,
% 38.15/38.35 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[9, 2])).
% 38.15/38.35 tff(11,plain,
% 38.15/38.35 ((~![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))))))),
% 38.15/38.35 inference(rewrite,[status(thm)],[])).
% 38.15/38.35 tff(12,plain,
% 38.15/38.35 ((~![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))))))),
% 38.15/38.35 inference(rewrite,[status(thm)],[])).
% 38.15/38.35 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/sandbox2/benchmark/theBenchmark.p','t54_filter_2')).
% 38.15/38.35 tff(14,plain,
% 38.15/38.35 (~![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)))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[13, 12])).
% 38.15/38.35 tff(15,plain,
% 38.15/38.35 (~![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)))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[14, 11])).
% 38.15/38.35 tff(16,plain,
% 38.15/38.35 (~![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)))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[15, 11])).
% 38.15/38.35 tff(17,plain,
% 38.15/38.35 (~![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)))))),
% 38.15/38.35 inference(modus_ponens,[status(thm)],[16, 11])).
% 38.15/38.35 tff(18,plain,(
% 38.15/38.35 ~((~((~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)))))),
% 38.15/38.35 inference(skolemize,[status(sab)],[17])).
% 38.15/38.35 tff(19,plain,
% 38.15/38.35 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 38.15/38.35 inference(or_elim,[status(thm)],[18])).
% 38.15/38.35 tff(20,plain,
% 38.15/38.35 (l3_lattices(A!0)),
% 38.15/38.35 inference(and_elim,[status(thm)],[19])).
% 38.15/38.35 tff(21,plain,
% 38.15/38.35 (((~![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))))),
% 38.15/38.35 inference(rewrite,[status(thm)],[])).
% 38.15/38.35 tff(22,plain,
% 38.15/38.35 ((~![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))))),
% 38.15/38.35 inference(quant_inst,[status(thm)],[])).
% 38.15/38.35 tff(23,plain,
% 38.15/38.35 ((~![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)))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[22, 21])).
% 38.20/38.35 tff(24,plain,
% 38.20/38.35 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 38.20/38.35 tff(25,plain,
% 38.20/38.35 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 38.20/38.35 inference(symmetry,[status(thm)],[24])).
% 38.20/38.35 tff(26,plain,
% 38.20/38.35 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v17_lattices(k1_lattice2(A!0))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[25])).
% 38.20/38.35 tff(27,plain,
% 38.20/38.35 (v17_lattices(k1_lattice2(A!0)) <=> v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.35 inference(symmetry,[status(thm)],[26])).
% 38.20/38.35 tff(28,plain,
% 38.20/38.35 ((~v17_lattices(k1_lattice2(A!0))) <=> (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[27])).
% 38.20/38.35 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)).
% 38.20/38.35 tff(30,plain,
% 38.20/38.35 ((~((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))))))),
% 38.20/38.35 inference(rewrite,[status(thm)],[])).
% 38.20/38.35 tff(31,plain,
% 38.20/38.35 (((~(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)))))),
% 38.20/38.35 inference(rewrite,[status(thm)],[])).
% 38.20/38.35 tff(32,plain,
% 38.20/38.35 (((~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)))))),
% 38.20/38.35 inference(rewrite,[status(thm)],[])).
% 38.20/38.35 tff(33,plain,
% 38.20/38.35 (((~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))))),
% 38.20/38.35 inference(rewrite,[status(thm)],[])).
% 38.20/38.35 tff(34,plain,
% 38.20/38.35 ((((~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))))))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[33, 32])).
% 38.20/38.35 tff(35,plain,
% 38.20/38.35 ((((~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)))))),
% 38.20/38.35 inference(transitivity,[status(thm)],[34, 31])).
% 38.20/38.35 tff(36,plain,
% 38.20/38.35 ((~(((~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))))))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[35])).
% 38.20/38.35 tff(37,plain,
% 38.20/38.35 ((~(((~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))))))),
% 38.20/38.35 inference(transitivity,[status(thm)],[36, 30])).
% 38.20/38.35 tff(38,plain,
% 38.20/38.35 (~(((~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))))),
% 38.20/38.35 inference(or_elim,[status(thm)],[18])).
% 38.20/38.35 tff(39,plain,
% 38.20/38.35 (~((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)))))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[38, 37])).
% 38.20/38.35 tff(40,plain,
% 38.20/38.35 (((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))))),
% 38.20/38.35 inference(tautology,[status(thm)],[])).
% 38.20/38.35 tff(41,plain,
% 38.20/38.35 ((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))))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[40, 39])).
% 38.20/38.35 tff(42,plain,
% 38.20/38.35 (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[41, 29])).
% 38.20/38.35 tff(43,plain,
% 38.20/38.35 (v10_lattices(A!0)),
% 38.20/38.35 inference(and_elim,[status(thm)],[19])).
% 38.20/38.35 tff(44,plain,
% 38.20/38.35 (~v3_struct_0(A!0)),
% 38.20/38.35 inference(and_elim,[status(thm)],[19])).
% 38.20/38.35 tff(45,plain,
% 38.20/38.35 ((~(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))),
% 38.20/38.35 inference(tautology,[status(thm)],[])).
% 38.20/38.35 tff(46,plain,
% 38.20/38.35 ((~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))) | (~v17_lattices(A!0))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[45, 44, 43, 20])).
% 38.20/38.35 tff(47,plain,
% 38.20/38.35 (~v17_lattices(A!0)),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[46, 42])).
% 38.20/38.35 tff(48,plain,
% 38.20/38.35 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))))),
% 38.20/38.35 inference(bind,[status(th)],[])).
% 38.20/38.35 tff(49,plain,
% 38.20/38.35 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))),
% 38.20/38.35 inference(quant_intro,[status(thm)],[48])).
% 38.20/38.35 tff(50,plain,
% 38.20/38.35 (^[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))))), trans(trans(monotonicity(rewrite((v15_lattices(A) & v16_lattices(A) & v11_lattices(A)) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))), ((v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))) <=> (v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))))), rewrite((v17_lattices(A) <=> (~((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))))) <=> (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))), ((v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))) <=> (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))), rewrite((~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))) <=> (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))), ((v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))) <=> (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_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))) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A))) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_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)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))))),
% 38.20/38.35 inference(bind,[status(th)],[])).
% 38.20/38.35 tff(51,plain,
% 38.20/38.35 (![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)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))),
% 38.20/38.35 inference(quant_intro,[status(thm)],[50])).
% 38.20/38.35 tff(52,plain,
% 38.20/38.35 (![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))))),
% 38.20/38.35 inference(rewrite,[status(thm)],[])).
% 38.20/38.35 tff(53,plain,
% 38.20/38.35 (^[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))))))),
% 38.20/38.35 inference(bind,[status(th)],[])).
% 38.20/38.35 tff(54,plain,
% 38.20/38.35 (![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))))),
% 38.20/38.35 inference(quant_intro,[status(thm)],[53])).
% 38.20/38.35 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/sandbox2/benchmark/theBenchmark.p','d20_lattices')).
% 38.20/38.35 tff(56,plain,
% 38.20/38.35 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[55, 54])).
% 38.20/38.35 tff(57,plain,
% 38.20/38.35 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[56, 52])).
% 38.20/38.35 tff(58,plain,(
% 38.20/38.35 ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v17_lattices(A) <=> (v15_lattices(A) & v16_lattices(A) & v11_lattices(A))))),
% 38.20/38.35 inference(skolemize,[status(sab)],[57])).
% 38.20/38.35 tff(59,plain,
% 38.20/38.35 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[58, 51])).
% 38.20/38.35 tff(60,plain,
% 38.20/38.35 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[59, 49])).
% 38.20/38.35 tff(61,plain,
% 38.20/38.35 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) <=> v17_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) <=> v17_lattices(A!0))))),
% 38.20/38.35 inference(rewrite,[status(thm)],[])).
% 38.20/38.35 tff(62,plain,
% 38.20/38.35 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) <=> v17_lattices(A!0))))),
% 38.20/38.35 inference(quant_inst,[status(thm)],[])).
% 38.20/38.35 tff(63,plain,
% 38.20/38.35 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) <=> v17_lattices(A!0)))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[62, 61])).
% 38.20/38.35 tff(64,plain,
% 38.20/38.35 (~(((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) <=> v17_lattices(A!0))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[63, 44, 20, 60])).
% 38.20/38.35 tff(65,plain,
% 38.20/38.35 ((((~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))) | v17_lattices(A!0)),
% 38.20/38.35 inference(tautology,[status(thm)],[])).
% 38.20/38.35 tff(66,plain,
% 38.20/38.35 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v17_lattices(A!0)),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[65, 64])).
% 38.20/38.35 tff(67,plain,
% 38.20/38.35 ((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[66, 47])).
% 38.20/38.35 tff(68,plain,
% 38.20/38.35 (v16_lattices(k1_lattice2(A!0)) <=> v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[24])).
% 38.20/38.35 tff(69,plain,
% 38.20/38.35 (v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v16_lattices(k1_lattice2(A!0))),
% 38.20/38.35 inference(symmetry,[status(thm)],[68])).
% 38.20/38.35 tff(70,plain,
% 38.20/38.35 ((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))),
% 38.20/38.35 inference(tautology,[status(thm)],[])).
% 38.20/38.35 tff(71,plain,
% 38.20/38.35 (v17_lattices(k1_lattice2(A!0))),
% 38.20/38.35 inference(unit_resolution,[status(thm)],[70, 29])).
% 38.20/38.35 tff(72,plain,
% 38.20/38.35 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.35 inference(modus_ponens,[status(thm)],[71, 27])).
% 38.20/38.35 tff(73,plain,
% 38.20/38.35 (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))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[25])).
% 38.20/38.35 tff(74,plain,
% 38.20/38.35 (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)))),
% 38.20/38.35 inference(symmetry,[status(thm)],[73])).
% 38.20/38.35 tff(75,plain,
% 38.20/38.35 ((~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))))),
% 38.20/38.35 inference(monotonicity,[status(thm)],[74])).
% 38.20/38.35 tff(76,plain,
% 38.20/38.35 (^[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)))))))),
% 38.20/38.35 inference(bind,[status(th)],[])).
% 38.20/38.35 tff(77,plain,
% 38.20/38.35 (![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))))))),
% 38.20/38.35 inference(quant_intro,[status(thm)],[76])).
% 38.20/38.35 tff(78,plain,
% 38.20/38.35 (^[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))))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(79,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[78])).
% 38.20/38.36 tff(80,plain,
% 38.20/38.36 (![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))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(81,plain,
% 38.20/38.36 (^[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))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(82,plain,
% 38.20/38.36 (![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))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[81])).
% 38.20/38.36 tff(83,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 38.20/38.36 tff(84,plain,
% 38.20/38.36 (![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))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[83, 82])).
% 38.20/38.36 tff(85,plain,
% 38.20/38.36 (![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))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[84, 80])).
% 38.20/38.36 tff(86,plain,(
% 38.20/38.36 ![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))))),
% 38.20/38.36 inference(skolemize,[status(sab)],[85])).
% 38.20/38.36 tff(87,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[86, 79])).
% 38.20/38.36 tff(88,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[87, 77])).
% 38.20/38.36 tff(89,plain,
% 38.20/38.36 (((~![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))))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(90,plain,
% 38.20/38.36 ((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))))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(91,plain,
% 38.20/38.36 (((~![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)))))))),
% 38.20/38.36 inference(monotonicity,[status(thm)],[90])).
% 38.20/38.36 tff(92,plain,
% 38.20/38.36 (((~![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))))))),
% 38.20/38.36 inference(transitivity,[status(thm)],[91, 89])).
% 38.20/38.36 tff(93,plain,
% 38.20/38.36 ((~![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))))))),
% 38.20/38.36 inference(quant_inst,[status(thm)],[])).
% 38.20/38.36 tff(94,plain,
% 38.20/38.36 ((~![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)))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[93, 92])).
% 38.20/38.36 tff(95,plain,
% 38.20/38.36 (~(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))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[94, 44, 43, 20, 88])).
% 38.20/38.36 tff(96,plain,
% 38.20/38.36 ((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)))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(97,plain,
% 38.20/38.36 (~v3_struct_0(k1_lattice2(A!0))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[96, 95])).
% 38.20/38.36 tff(98,plain,
% 38.20/38.36 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[97, 75])).
% 38.20/38.36 tff(99,plain,
% 38.20/38.36 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> l3_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(monotonicity,[status(thm)],[25])).
% 38.20/38.36 tff(100,plain,
% 38.20/38.36 (l3_lattices(k1_lattice2(A!0)) <=> l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.36 inference(symmetry,[status(thm)],[99])).
% 38.20/38.36 tff(101,plain,
% 38.20/38.36 (^[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)))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(102,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[101])).
% 38.20/38.36 tff(103,plain,
% 38.20/38.36 (^[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)))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(104,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[103])).
% 38.20/38.36 tff(105,plain,
% 38.20/38.36 (![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))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(106,plain,
% 38.20/38.36 (^[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)))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(107,plain,
% 38.20/38.36 (![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))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[106])).
% 38.20/38.36 tff(108,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice2')).
% 38.20/38.36 tff(109,plain,
% 38.20/38.36 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[108, 107])).
% 38.20/38.36 tff(110,plain,
% 38.20/38.36 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[109, 105])).
% 38.20/38.36 tff(111,plain,(
% 38.20/38.36 ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 38.20/38.36 inference(skolemize,[status(sab)],[110])).
% 38.20/38.36 tff(112,plain,
% 38.20/38.36 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[111, 104])).
% 38.20/38.36 tff(113,plain,
% 38.20/38.36 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[112, 102])).
% 38.20/38.36 tff(114,plain,
% 38.20/38.36 (((~![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))))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(115,plain,
% 38.20/38.36 (((~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))))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(116,plain,
% 38.20/38.36 (((~![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)))))))),
% 38.20/38.36 inference(monotonicity,[status(thm)],[115])).
% 38.20/38.36 tff(117,plain,
% 38.20/38.36 (((~![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))))))),
% 38.20/38.36 inference(transitivity,[status(thm)],[116, 114])).
% 38.20/38.36 tff(118,plain,
% 38.20/38.36 ((~![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))))))),
% 38.20/38.36 inference(quant_inst,[status(thm)],[])).
% 38.20/38.36 tff(119,plain,
% 38.20/38.36 ((~![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)))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[118, 117])).
% 38.20/38.36 tff(120,plain,
% 38.20/38.36 (~((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[119, 20, 113])).
% 38.20/38.36 tff(121,plain,
% 38.20/38.36 (((~l3_lattices(k1_lattice2(A!0))) | (~v3_lattices(k1_lattice2(A!0)))) | l3_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(122,plain,
% 38.20/38.36 (l3_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[121, 120])).
% 38.20/38.36 tff(123,plain,
% 38.20/38.36 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[122, 100])).
% 38.20/38.36 tff(124,plain,
% 38.20/38.36 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_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)))) | (~(((~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))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_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)))) | (~(((~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))))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(125,plain,
% 38.20/38.36 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_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)))) | (~(((~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))))))),
% 38.20/38.36 inference(quant_inst,[status(thm)],[])).
% 38.20/38.36 tff(126,plain,
% 38.20/38.36 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(((~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A))) <=> v17_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)))) | (~(((~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)))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[125, 124])).
% 38.20/38.36 tff(127,plain,
% 38.20/38.36 (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)))) | (~(((~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)))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[126, 60])).
% 38.20/38.36 tff(128,plain,
% 38.20/38.36 (~(((~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))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[127, 123, 98])).
% 38.20/38.36 tff(129,plain,
% 38.20/38.36 ((((~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)))))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(130,plain,
% 38.20/38.36 ((~((~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))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[129, 128])).
% 38.20/38.36 tff(131,plain,
% 38.20/38.36 (~((~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)))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[130, 72])).
% 38.20/38.36 tff(132,plain,
% 38.20/38.36 (((~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)))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(133,plain,
% 38.20/38.36 (v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[132, 131])).
% 38.20/38.36 tff(134,plain,
% 38.20/38.36 (v16_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[133, 69])).
% 38.20/38.36 tff(135,plain,
% 38.20/38.36 (v15_lattices(k1_lattice2(A!0)) <=> v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.36 inference(monotonicity,[status(thm)],[24])).
% 38.20/38.36 tff(136,plain,
% 38.20/38.36 (v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v15_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(symmetry,[status(thm)],[135])).
% 38.20/38.36 tff(137,plain,
% 38.20/38.36 (((~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)))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(138,plain,
% 38.20/38.36 (v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[137, 131])).
% 38.20/38.36 tff(139,plain,
% 38.20/38.36 (v15_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[138, 136])).
% 38.20/38.36 tff(140,plain,
% 38.20/38.36 ((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))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(141,plain,
% 38.20/38.36 (v10_lattices(k1_lattice2(A!0))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[140, 95])).
% 38.20/38.36 tff(142,plain,
% 38.20/38.36 ((~(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)))),
% 38.20/38.36 inference(tautology,[status(thm)],[])).
% 38.20/38.36 tff(143,plain,
% 38.20/38.36 ((~(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)))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[142, 97, 141])).
% 38.20/38.36 tff(144,plain,
% 38.20/38.36 ((~(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)))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[143, 122])).
% 38.20/38.36 tff(145,plain,
% 38.20/38.36 (~(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))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[144, 139, 134])).
% 38.20/38.36 tff(146,plain,
% 38.20/38.36 (^[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)))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(147,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[146])).
% 38.20/38.36 tff(148,plain,
% 38.20/38.36 (^[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))))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(149,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[148])).
% 38.20/38.36 tff(150,plain,
% 38.20/38.36 (![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)))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(151,plain,
% 38.20/38.36 (^[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)))))))),
% 38.20/38.36 inference(bind,[status(th)],[])).
% 38.20/38.36 tff(152,plain,
% 38.20/38.36 (![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)))))),
% 38.20/38.36 inference(quant_intro,[status(thm)],[151])).
% 38.20/38.36 tff(153,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/sandbox2/benchmark/theBenchmark.p','t53_filter_2')).
% 38.20/38.36 tff(154,plain,
% 38.20/38.36 (![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)))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[153, 152])).
% 38.20/38.36 tff(155,plain,
% 38.20/38.36 (![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)))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[154, 150])).
% 38.20/38.36 tff(156,plain,(
% 38.20/38.36 ![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)))))),
% 38.20/38.36 inference(skolemize,[status(sab)],[155])).
% 38.20/38.36 tff(157,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[156, 149])).
% 38.20/38.36 tff(158,plain,
% 38.20/38.36 (![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))))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[157, 147])).
% 38.20/38.36 tff(159,plain,
% 38.20/38.36 (((~![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))))))),
% 38.20/38.36 inference(rewrite,[status(thm)],[])).
% 38.20/38.36 tff(160,plain,
% 38.20/38.36 ((~![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))))))),
% 38.20/38.36 inference(quant_inst,[status(thm)],[])).
% 38.20/38.36 tff(161,plain,
% 38.20/38.36 ((~![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)))))),
% 38.20/38.36 inference(modus_ponens,[status(thm)],[160, 159])).
% 38.20/38.36 tff(162,plain,
% 38.20/38.36 ((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))))),
% 38.20/38.36 inference(unit_resolution,[status(thm)],[161, 44, 43, 20, 158])).
% 38.20/38.36 tff(163,plain,
% 38.20/38.36 ((~((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))))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(164,plain,
% 38.20/38.37 ((~(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))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[163, 162])).
% 38.20/38.37 tff(165,plain,
% 38.20/38.37 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[164, 145])).
% 38.20/38.37 tff(166,plain,
% 38.20/38.37 ((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)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(167,plain,
% 38.20/38.37 (v16_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[166, 165])).
% 38.20/38.37 tff(168,plain,
% 38.20/38.37 (v11_lattices(k1_lattice2(A!0)) <=> v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.37 inference(monotonicity,[status(thm)],[24])).
% 38.20/38.37 tff(169,plain,
% 38.20/38.37 (v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v11_lattices(k1_lattice2(A!0))),
% 38.20/38.37 inference(symmetry,[status(thm)],[168])).
% 38.20/38.37 tff(170,plain,
% 38.20/38.37 (((~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)))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(171,plain,
% 38.20/38.37 (v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[170, 131])).
% 38.20/38.37 tff(172,plain,
% 38.20/38.37 (v11_lattices(k1_lattice2(A!0))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[171, 169])).
% 38.20/38.37 tff(173,plain,
% 38.20/38.37 ((~(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)))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(174,plain,
% 38.20/38.37 ((~(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)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[173, 97, 141])).
% 38.20/38.37 tff(175,plain,
% 38.20/38.37 ((~(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)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[174, 122])).
% 38.20/38.37 tff(176,plain,
% 38.20/38.37 (~(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))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[175, 172])).
% 38.20/38.37 tff(177,plain,
% 38.20/38.37 (^[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)))))))),
% 38.20/38.37 inference(bind,[status(th)],[])).
% 38.20/38.37 tff(178,plain,
% 38.20/38.37 (![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))))))),
% 38.20/38.37 inference(quant_intro,[status(thm)],[177])).
% 38.20/38.37 tff(179,plain,
% 38.20/38.37 (^[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))))))))),
% 38.20/38.37 inference(bind,[status(th)],[])).
% 38.20/38.37 tff(180,plain,
% 38.20/38.37 (![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))))))),
% 38.20/38.37 inference(quant_intro,[status(thm)],[179])).
% 38.20/38.37 tff(181,plain,
% 38.20/38.37 (![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)))))),
% 38.20/38.37 inference(rewrite,[status(thm)],[])).
% 38.20/38.37 tff(182,plain,
% 38.20/38.37 (^[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)))))))),
% 38.20/38.37 inference(bind,[status(th)],[])).
% 38.20/38.37 tff(183,plain,
% 38.20/38.37 (![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)))))),
% 38.20/38.37 inference(quant_intro,[status(thm)],[182])).
% 38.20/38.37 tff(184,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/sandbox2/benchmark/theBenchmark.p','t65_lattice2')).
% 38.20/38.37 tff(185,plain,
% 38.20/38.37 (![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)))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[184, 183])).
% 38.20/38.37 tff(186,plain,
% 38.20/38.37 (![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)))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[185, 181])).
% 38.20/38.37 tff(187,plain,(
% 38.20/38.37 ![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)))))),
% 38.20/38.37 inference(skolemize,[status(sab)],[186])).
% 38.20/38.37 tff(188,plain,
% 38.20/38.37 (![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))))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[187, 180])).
% 38.20/38.37 tff(189,plain,
% 38.20/38.37 (![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))))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[188, 178])).
% 38.20/38.37 tff(190,plain,
% 38.20/38.37 (((~![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))))))),
% 38.20/38.37 inference(rewrite,[status(thm)],[])).
% 38.20/38.37 tff(191,plain,
% 38.20/38.37 ((~![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))))))),
% 38.20/38.37 inference(quant_inst,[status(thm)],[])).
% 38.20/38.37 tff(192,plain,
% 38.20/38.37 ((~![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)))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[191, 190])).
% 38.20/38.37 tff(193,plain,
% 38.20/38.37 ((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))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[192, 44, 43, 20, 189])).
% 38.20/38.37 tff(194,plain,
% 38.20/38.37 ((~((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))))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(195,plain,
% 38.20/38.37 ((~(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))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[194, 193])).
% 38.20/38.37 tff(196,plain,
% 38.20/38.37 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[195, 176])).
% 38.20/38.37 tff(197,plain,
% 38.20/38.37 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0))) | v11_lattices(A!0)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(198,plain,
% 38.20/38.37 (v11_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[197, 196])).
% 38.20/38.37 tff(199,plain,
% 38.20/38.37 ((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)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(200,plain,
% 38.20/38.37 (v15_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[199, 165])).
% 38.20/38.37 tff(201,plain,
% 38.20/38.37 ((~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(202,plain,
% 38.20/38.37 ($false),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[201, 200, 198, 167, 67])).
% 38.20/38.37 tff(203,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,[]))).
% 38.20/38.37 tff(204,plain,
% 38.20/38.37 ((~(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)))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(205,plain,
% 38.20/38.37 ((~(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)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[204, 97, 141, 122])).
% 38.20/38.37 tff(206,plain,
% 38.20/38.37 (~v17_lattices(k1_lattice2(A!0))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[205, 203])).
% 38.20/38.37 tff(207,plain,
% 38.20/38.37 (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[206, 28])).
% 38.20/38.37 tff(208,plain,
% 38.20/38.37 (((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)))))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(209,plain,
% 38.20/38.37 ((~(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)))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[208, 39])).
% 38.20/38.37 tff(210,plain,
% 38.20/38.37 (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[209, 203])).
% 38.20/38.37 tff(211,plain,
% 38.20/38.37 ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0))) | v17_lattices(A!0)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(212,plain,
% 38.20/38.37 (v17_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[211, 210])).
% 38.20/38.37 tff(213,plain,
% 38.20/38.37 ((((~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)))) | (~v17_lattices(A!0))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(214,plain,
% 38.20/38.37 ((~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[213, 64])).
% 38.20/38.37 tff(215,plain,
% 38.20/38.37 (~((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[214, 212])).
% 38.20/38.37 tff(216,plain,
% 38.20/38.37 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v15_lattices(A!0)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(217,plain,
% 38.20/38.37 (v15_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[216, 215])).
% 38.20/38.37 tff(218,plain,
% 38.20/38.37 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v16_lattices(A!0)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(219,plain,
% 38.20/38.37 (v16_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[218, 215])).
% 38.20/38.37 tff(220,plain,
% 38.20/38.37 ((~(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))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(221,plain,
% 38.20/38.37 ((~(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))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[220, 44, 43, 20])).
% 38.20/38.37 tff(222,plain,
% 38.20/38.37 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[221, 219, 217])).
% 38.20/38.37 tff(223,plain,
% 38.20/38.37 ((~((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)))))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(224,plain,
% 38.20/38.37 ((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)))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[223, 162])).
% 38.20/38.37 tff(225,plain,
% 38.20/38.37 (~(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))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[224, 222])).
% 38.20/38.37 tff(226,plain,
% 38.20/38.37 ((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))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(227,plain,
% 38.20/38.37 (v16_lattices(k1_lattice2(A!0))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[226, 225])).
% 38.20/38.37 tff(228,plain,
% 38.20/38.37 (v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[227, 68])).
% 38.20/38.37 tff(229,plain,
% 38.20/38.37 (((~v15_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0))) | v11_lattices(A!0)),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(230,plain,
% 38.20/38.37 (v11_lattices(A!0)),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[229, 215])).
% 38.20/38.37 tff(231,plain,
% 38.20/38.37 ((~(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))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(232,plain,
% 38.20/38.37 ((~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))) | (~v11_lattices(A!0))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[231, 44, 43, 20])).
% 38.20/38.37 tff(233,plain,
% 38.20/38.37 (~(v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[232, 230])).
% 38.20/38.37 tff(234,plain,
% 38.20/38.37 ((~((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)))))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(235,plain,
% 38.20/38.37 ((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)))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[234, 193])).
% 38.20/38.37 tff(236,plain,
% 38.20/38.37 (~(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))))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[235, 233])).
% 38.20/38.37 tff(237,plain,
% 38.20/38.37 ((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))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(238,plain,
% 38.20/38.37 (v11_lattices(k1_lattice2(A!0))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[237, 236])).
% 38.20/38.37 tff(239,plain,
% 38.20/38.37 (v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[238, 168])).
% 38.20/38.37 tff(240,plain,
% 38.20/38.37 ((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))),
% 38.20/38.37 inference(tautology,[status(thm)],[])).
% 38.20/38.37 tff(241,plain,
% 38.20/38.37 (v15_lattices(k1_lattice2(A!0))),
% 38.20/38.37 inference(unit_resolution,[status(thm)],[240, 225])).
% 38.20/38.37 tff(242,plain,
% 38.20/38.37 (v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[241, 135])).
% 38.20/38.37 tff(243,plain,
% 38.20/38.37 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A))))))),
% 38.20/38.37 inference(bind,[status(th)],[])).
% 38.20/38.37 tff(244,plain,
% 38.20/38.37 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 38.20/38.37 inference(quant_intro,[status(thm)],[243])).
% 38.20/38.37 tff(245,plain,
% 38.20/38.37 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v17_lattices(A)) <=> (~(v3_struct_0(A) | (~v17_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)) <=> (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))) <=> (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))), ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) <=> (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), ((((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ((~(v3_struct_0(A) | (~v17_lattices(A)))) | (~l3_lattices(A)) | (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))))), rewrite(((~(v3_struct_0(A) | (~v17_lattices(A)))) | (~l3_lattices(A)) | (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))), ((((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))))),
% 38.20/38.37 inference(bind,[status(th)],[])).
% 38.20/38.37 tff(246,plain,
% 38.20/38.37 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 38.20/38.37 inference(quant_intro,[status(thm)],[245])).
% 38.20/38.37 tff(247,plain,
% 38.20/38.37 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 38.20/38.37 inference(rewrite,[status(thm)],[])).
% 38.20/38.37 tff(248,plain,
% 38.20/38.37 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))) <=> ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A)))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))) <=> ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A))))), ((l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A)))) <=> (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))), ((l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A)))) <=> (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))))),
% 38.20/38.37 inference(bind,[status(th)],[])).
% 38.20/38.37 tff(249,plain,
% 38.20/38.37 (![A: $i] : (l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 38.20/38.37 inference(quant_intro,[status(thm)],[248])).
% 38.20/38.37 tff(250,axiom,(![A: $i] : (l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc6_lattices')).
% 38.20/38.37 tff(251,plain,
% 38.20/38.37 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[250, 249])).
% 38.20/38.37 tff(252,plain,
% 38.20/38.37 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[251, 247])).
% 38.20/38.37 tff(253,plain,(
% 38.20/38.37 ![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 38.20/38.37 inference(skolemize,[status(sab)],[252])).
% 38.20/38.37 tff(254,plain,
% 38.20/38.37 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[253, 246])).
% 38.20/38.37 tff(255,plain,
% 38.20/38.37 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 38.20/38.37 inference(modus_ponens,[status(thm)],[254, 244])).
% 38.20/38.37 tff(256,plain,
% 38.20/38.37 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_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)))) | (~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)))) | (~(v3_struct_0(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)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_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)))) | (~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)))) | (~(v3_struct_0(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)))))))),
% 38.39/38.58 inference(rewrite,[status(thm)],[])).
% 38.39/38.58 tff(257,plain,
% 38.39/38.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_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)))) | (~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)))) | (~(v3_struct_0(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)))))))),
% 38.39/38.58 inference(quant_inst,[status(thm)],[])).
% 38.39/38.58 tff(258,plain,
% 38.39/38.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v15_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v11_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v16_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 38.39/38.58 inference(modus_ponens,[status(thm)],[257, 256])).
% 38.39/38.58 tff(259,plain,
% 38.39/38.58 (~(v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 38.39/38.58 inference(unit_resolution,[status(thm)],[258, 255, 98, 123, 242, 239, 228])).
% 38.39/38.58 tff(260,plain,
% 38.39/38.58 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 38.39/38.58 inference(tautology,[status(thm)],[])).
% 38.39/38.58 tff(261,plain,
% 38.39/38.58 ($false),
% 38.39/38.58 inference(unit_resolution,[status(thm)],[260, 259, 207])).
% 38.39/38.58 % SZS output end Proof
% 38.39/38.58 % E exiting
%------------------------------------------------------------------------------