%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT301+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:14:14 AM UTC 2025
% Result : Theorem 0.21s 0.56s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LAT301+1 : TPTP v9.0.0. Released v3.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:10:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.56 % SZS status Theorem
% 0.21/0.56 % SZS output start Proof
% 0.21/0.56 tff(m1_filter_0_type, type, (
% 0.21/0.56 m1_filter_0: ( $i * $i ) > $o)).
% 0.21/0.56 tff(g3_lattices_type, type, (
% 0.21/0.56 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.21/0.56 tff(u2_lattices_type, type, (
% 0.21/0.56 u2_lattices: $i > $i)).
% 0.21/0.56 tff(tptp_fun_A_0_type, type, (
% 0.21/0.56 tptp_fun_A_0: $i)).
% 0.21/0.56 tff(u1_lattices_type, type, (
% 0.21/0.56 u1_lattices: $i > $i)).
% 0.21/0.56 tff(u1_struct_0_type, type, (
% 0.21/0.56 u1_struct_0: $i > $i)).
% 0.21/0.56 tff(k7_filter_2_type, type, (
% 0.21/0.56 k7_filter_2: ( $i * $i ) > $i)).
% 0.21/0.56 tff(tptp_fun_B_1_type, type, (
% 0.21/0.56 tptp_fun_B_1: $i)).
% 0.21/0.56 tff(m1_filter_2_type, type, (
% 0.21/0.56 m1_filter_2: ( $i * $i ) > $o)).
% 0.21/0.56 tff(v10_lattices_type, type, (
% 0.21/0.56 v10_lattices: $i > $o)).
% 0.21/0.56 tff(k1_lattice2_type, type, (
% 0.21/0.56 k1_lattice2: $i > $i)).
% 0.21/0.56 tff(l3_lattices_type, type, (
% 0.21/0.56 l3_lattices: $i > $o)).
% 0.21/0.56 tff(m2_filter_2_type, type, (
% 0.21/0.56 m2_filter_2: ( $i * $i ) > $o)).
% 0.21/0.56 tff(r2_hidden_type, type, (
% 0.21/0.56 r2_hidden: ( $i * $i ) > $o)).
% 0.21/0.56 tff(k5_lattices_type, type, (
% 0.21/0.56 k5_lattices: $i > $i)).
% 0.21/0.56 tff(v13_lattices_type, type, (
% 0.21/0.56 v13_lattices: $i > $o)).
% 0.21/0.56 tff(v3_struct_0_type, type, (
% 0.21/0.56 v3_struct_0: $i > $o)).
% 0.21/0.56 tff(v9_lattices_type, type, (
% 0.21/0.56 v9_lattices: $i > $o)).
% 0.21/0.56 tff(v8_lattices_type, type, (
% 0.21/0.56 v8_lattices: $i > $o)).
% 0.21/0.56 tff(v7_lattices_type, type, (
% 0.21/0.56 v7_lattices: $i > $o)).
% 0.21/0.56 tff(v6_lattices_type, type, (
% 0.21/0.56 v6_lattices: $i > $o)).
% 0.21/0.56 tff(v5_lattices_type, type, (
% 0.21/0.56 v5_lattices: $i > $o)).
% 0.21/0.56 tff(v4_lattices_type, type, (
% 0.21/0.56 v4_lattices: $i > $o)).
% 0.21/0.56 tff(v3_lattices_type, type, (
% 0.21/0.56 v3_lattices: $i > $o)).
% 0.21/0.56 tff(k15_filter_2_type, type, (
% 0.21/0.56 k15_filter_2: ( $i * $i ) > $i)).
% 0.21/0.56 tff(k6_lattices_type, type, (
% 0.21/0.56 k6_lattices: $i > $i)).
% 0.21/0.56 tff(m1_subset_1_type, type, (
% 0.21/0.56 m1_subset_1: ( $i * $i ) > $o)).
% 0.21/0.56 tff(k1_zfmisc_1_type, type, (
% 0.21/0.56 k1_zfmisc_1: $i > $i)).
% 0.21/0.56 tff(m2_lattice4_type, type, (
% 0.21/0.56 m2_lattice4: ( $i * $i ) > $o)).
% 0.21/0.56 tff(v1_xboole_0_type, type, (
% 0.21/0.56 v1_xboole_0: $i > $o)).
% 0.21/0.56 tff(v14_lattices_type, type, (
% 0.21/0.56 v14_lattices: $i > $o)).
% 0.21/0.56 tff(1,plain,
% 0.21/0.56 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(2,plain,
% 0.21/0.56 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.56 tff(3,plain,
% 0.21/0.56 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(4,plain,
% 0.21/0.56 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(5,plain,
% 0.21/0.56 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.56 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 0.21/0.56 tff(7,plain,
% 0.21/0.56 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.56 tff(8,plain,
% 0.21/0.56 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.56 tff(9,plain,(
% 0.21/0.56 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(skolemize,[status(sab)],[8])).
% 0.21/0.56 tff(10,plain,
% 0.21/0.56 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.56 tff(11,plain,
% 0.21/0.56 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(12,plain,
% 0.21/0.56 ((~(r2_hidden(k5_lattices(A!0), B!1) | (~v13_lattices(A!0)) | (~m2_filter_2(B!1, A!0)))) <=> (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(13,plain,
% 0.21/0.56 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(r2_hidden(k5_lattices(A!0), B!1) | (~v13_lattices(A!0)) | (~m2_filter_2(B!1, A!0))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0)))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[12])).
% 0.21/0.56 tff(14,plain,
% 0.21/0.56 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(r2_hidden(k5_lattices(A!0), B!1) | (~v13_lattices(A!0)) | (~m2_filter_2(B!1, A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0)))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[13, 11])).
% 0.21/0.56 tff(15,plain,
% 0.21/0.56 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(16,plain,
% 0.21/0.56 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (v13_lattices(A) => r2_hidden(k5_lattices(A), B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(17,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (v13_lattices(A) => r2_hidden(k5_lattices(A), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_filter_2')).
% 0.21/0.56 tff(18,plain,
% 0.21/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.21/0.56 tff(19,plain,
% 0.21/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.21/0.56 tff(20,plain,
% 0.21/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.21/0.56 tff(21,plain,
% 0.21/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k5_lattices(A), B) | (~v13_lattices(A)) | (~m2_filter_2(B, A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.21/0.56 tff(22,plain,
% 0.21/0.56 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.21/0.56 tff(23,plain,
% 0.21/0.56 (l3_lattices(A!0)),
% 0.21/0.56 inference(and_elim,[status(thm)],[22])).
% 0.21/0.56 tff(24,plain,
% 0.21/0.56 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(25,plain,
% 0.21/0.56 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(26,plain,
% 0.21/0.56 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.56 tff(27,plain,
% 0.21/0.56 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.21/0.56 tff(28,plain,
% 0.21/0.56 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.21/0.56 inference(symmetry,[status(thm)],[27])).
% 0.21/0.56 tff(29,plain,
% 0.21/0.56 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.56 tff(30,plain,
% 0.21/0.56 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.56 inference(symmetry,[status(thm)],[29])).
% 0.21/0.56 tff(31,plain,
% 0.21/0.56 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(32,plain,
% 0.21/0.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.56 tff(33,plain,
% 0.21/0.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(34,plain,
% 0.21/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.56 tff(35,plain,
% 0.21/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(36,plain,
% 0.21/0.56 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(37,plain,
% 0.21/0.56 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.56 tff(38,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 0.21/0.56 tff(39,plain,
% 0.21/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.56 tff(40,plain,
% 0.21/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.56 tff(41,plain,(
% 0.21/0.56 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.21/0.56 inference(skolemize,[status(sab)],[40])).
% 0.21/0.56 tff(42,plain,
% 0.21/0.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.56 tff(43,plain,
% 0.21/0.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.21/0.56 tff(44,plain,
% 0.21/0.56 (v10_lattices(A!0)),
% 0.21/0.56 inference(and_elim,[status(thm)],[22])).
% 0.21/0.56 tff(45,plain,
% 0.21/0.56 (~v3_struct_0(A!0)),
% 0.21/0.56 inference(and_elim,[status(thm)],[22])).
% 0.21/0.56 tff(46,plain,
% 0.21/0.56 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(47,plain,
% 0.21/0.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(48,plain,
% 0.21/0.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.56 tff(49,plain,
% 0.21/0.56 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[48, 45, 44, 23, 43])).
% 0.21/0.56 tff(50,plain,
% 0.21/0.56 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(51,plain,
% 0.21/0.56 (v10_lattices(k1_lattice2(A!0))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.21/0.56 tff(52,plain,
% 0.21/0.56 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[51, 30])).
% 0.21/0.56 tff(53,plain,
% 0.21/0.56 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.56 tff(54,plain,
% 0.21/0.56 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.56 inference(symmetry,[status(thm)],[53])).
% 0.21/0.56 tff(55,plain,
% 0.21/0.56 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[54])).
% 0.21/0.56 tff(56,plain,
% 0.21/0.56 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 0.21/0.56 inference(tautology,[status(thm)],[])).
% 0.21/0.56 tff(57,plain,
% 0.21/0.56 (~v3_struct_0(k1_lattice2(A!0))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[56, 49])).
% 0.21/0.56 tff(58,plain,
% 0.21/0.56 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[57, 55])).
% 0.21/0.56 tff(59,plain,
% 0.21/0.56 (l3_lattices(k1_lattice2(A!0)) <=> l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[27])).
% 0.21/0.56 tff(60,plain,
% 0.21/0.56 (^[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)))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(61,plain,
% 0.21/0.56 (![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))))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.56 tff(62,plain,
% 0.21/0.56 (^[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)))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(63,plain,
% 0.21/0.56 (![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))))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.56 tff(64,plain,
% 0.21/0.56 (![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))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(65,plain,
% 0.21/0.56 (^[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)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(66,plain,
% 0.21/0.57 (![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))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.57 tff(67,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lattice2')).
% 0.21/0.57 tff(68,plain,
% 0.21/0.57 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.57 tff(69,plain,
% 0.21/0.57 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.57 tff(70,plain,(
% 0.21/0.57 ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 0.21/0.57 inference(skolemize,[status(sab)],[69])).
% 0.21/0.57 tff(71,plain,
% 0.21/0.57 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.57 tff(72,plain,
% 0.21/0.57 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.21/0.57 tff(73,plain,
% 0.21/0.57 (((~![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)) | (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(74,plain,
% 0.21/0.57 ((~![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))))))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(75,plain,
% 0.21/0.57 ((~![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)))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.57 tff(76,plain,
% 0.21/0.57 (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[75, 23, 72])).
% 0.21/0.57 tff(77,plain,
% 0.21/0.57 (((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))) | l3_lattices(k1_lattice2(A!0))),
% 0.21/0.57 inference(tautology,[status(thm)],[])).
% 0.21/0.57 tff(78,plain,
% 0.21/0.57 (l3_lattices(k1_lattice2(A!0))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.21/0.57 tff(79,plain,
% 0.21/0.57 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[78, 59])).
% 0.21/0.57 tff(80,plain,
% 0.21/0.57 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(81,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.57 tff(82,plain,
% 0.21/0.57 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(83,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.57 tff(84,plain,
% 0.21/0.57 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(85,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.57 tff(86,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.57 inference(transitivity,[status(thm)],[85, 83])).
% 0.21/0.57 tff(87,plain,
% 0.21/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(88,plain,
% 0.21/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.57 tff(89,plain,
% 0.21/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(90,plain,
% 0.21/0.57 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(91,plain,
% 0.21/0.57 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[90])).
% 0.21/0.57 tff(92,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 0.21/0.57 tff(93,plain,
% 0.21/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.57 tff(94,plain,
% 0.21/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.21/0.57 tff(95,plain,(
% 0.21/0.57 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(skolemize,[status(sab)],[94])).
% 0.21/0.57 tff(96,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.21/0.57 tff(97,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[96, 86])).
% 0.21/0.57 tff(98,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[97, 81])).
% 0.21/0.57 tff(99,plain,
% 0.21/0.57 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(100,plain,
% 0.21/0.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(101,plain,
% 0.21/0.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.57 tff(102,plain,
% 0.21/0.57 (![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[101, 98, 79, 58, 52])).
% 0.21/0.57 tff(103,plain,
% 0.21/0.57 ((~![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(104,plain,
% 0.21/0.57 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.21/0.57 tff(105,plain,
% 0.21/0.57 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(106,plain,
% 0.21/0.57 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[105])).
% 0.21/0.57 tff(107,plain,
% 0.21/0.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(108,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.57 tff(109,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(110,plain,
% 0.21/0.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(111,plain,
% 0.21/0.57 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.57 tff(112,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 0.21/0.57 tff(113,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.57 tff(114,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.57 tff(115,plain,(
% 0.21/0.57 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 0.21/0.57 inference(skolemize,[status(sab)],[114])).
% 0.21/0.57 tff(116,plain,
% 0.21/0.57 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.21/0.57 tff(117,plain,
% 0.21/0.57 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.21/0.57 tff(118,plain,
% 0.21/0.57 (~((~v13_lattices(A!0)) | r2_hidden(k5_lattices(A!0), B!1) | (~m2_filter_2(B!1, A!0)))),
% 0.21/0.57 inference(and_elim,[status(thm)],[22])).
% 0.21/0.57 tff(119,plain,
% 0.21/0.57 (m2_filter_2(B!1, A!0)),
% 0.21/0.57 inference(or_elim,[status(thm)],[118])).
% 0.21/0.57 tff(120,plain,
% 0.21/0.57 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(121,plain,
% 0.21/0.57 ((v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(122,plain,
% 0.21/0.57 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[121])).
% 0.21/0.57 tff(123,plain,
% 0.21/0.57 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 0.21/0.57 inference(transitivity,[status(thm)],[122, 120])).
% 0.21/0.57 tff(124,plain,
% 0.21/0.57 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(125,plain,
% 0.21/0.57 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.57 tff(126,plain,
% 0.21/0.57 (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[125, 45, 44, 23, 119, 117])).
% 0.21/0.57 tff(127,plain,
% 0.21/0.57 (k7_filter_2(A!0, B!1) = k15_filter_2(A!0, B!1)),
% 0.21/0.57 inference(symmetry,[status(thm)],[126])).
% 0.21/0.57 tff(128,plain,
% 0.21/0.57 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[127, 28])).
% 0.21/0.57 tff(129,plain,
% 0.21/0.57 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) <=> m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.57 inference(symmetry,[status(thm)],[128])).
% 0.21/0.57 tff(130,plain,
% 0.21/0.57 (^[A: $i, B: $i] : refl((m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(131,plain,
% 0.21/0.57 (![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.57 tff(132,plain,
% 0.21/0.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(133,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.57 tff(134,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(135,plain,
% 0.21/0.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(136,plain,
% 0.21/0.57 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.57 tff(137,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k15_filter_2')).
% 0.21/0.57 tff(138,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.57 tff(139,plain,
% 0.21/0.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.21/0.57 tff(140,plain,(
% 0.21/0.57 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 0.21/0.57 inference(skolemize,[status(sab)],[139])).
% 0.21/0.57 tff(141,plain,
% 0.21/0.57 (![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.21/0.57 tff(142,plain,
% 0.21/0.57 (![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[141, 131])).
% 0.21/0.57 tff(143,plain,
% 0.21/0.57 (((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(144,plain,
% 0.21/0.57 ((m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(145,plain,
% 0.21/0.57 (((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.57 tff(146,plain,
% 0.21/0.57 (((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 0.21/0.57 inference(transitivity,[status(thm)],[145, 143])).
% 0.21/0.57 tff(147,plain,
% 0.21/0.57 ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(148,plain,
% 0.21/0.57 ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.57 tff(149,plain,
% 0.21/0.57 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[148, 45, 44, 23, 119, 142])).
% 0.21/0.57 tff(150,plain,
% 0.21/0.57 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[149, 129])).
% 0.21/0.57 tff(151,plain,
% 0.21/0.57 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(152,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[151])).
% 0.21/0.57 tff(153,plain,
% 0.21/0.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(154,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[153])).
% 0.21/0.57 tff(155,plain,
% 0.21/0.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.21/0.57 inference(transitivity,[status(thm)],[154, 152])).
% 0.21/0.57 tff(156,plain,
% 0.21/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(157,plain,
% 0.21/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[156])).
% 0.21/0.57 tff(158,plain,
% 0.21/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(159,plain,
% 0.21/0.57 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(160,plain,
% 0.21/0.58 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[159])).
% 0.21/0.58 tff(161,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.21/0.58 tff(162,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.58 tff(163,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.21/0.58 tff(164,plain,(
% 0.21/0.58 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.21/0.58 inference(skolemize,[status(sab)],[163])).
% 0.21/0.58 tff(165,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.21/0.58 tff(166,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[165, 155])).
% 0.21/0.58 tff(167,plain,
% 0.21/0.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(168,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(169,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.58 tff(170,plain,
% 0.21/0.58 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[169, 45, 44, 23, 166])).
% 0.21/0.58 tff(171,plain,
% 0.21/0.58 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(172,plain,
% 0.21/0.58 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(173,plain,
% 0.21/0.58 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.58 tff(174,plain,
% 0.21/0.58 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[173, 119, 170])).
% 0.21/0.58 tff(175,plain,
% 0.21/0.58 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 0.21/0.58 inference(tautology,[status(thm)],[])).
% 0.21/0.58 tff(176,plain,
% 0.21/0.58 (m2_lattice4(B!1, A!0)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.21/0.58 tff(177,plain,
% 0.21/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(178,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[177])).
% 0.21/0.58 tff(179,plain,
% 0.21/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(180,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.58 tff(181,plain,
% 0.21/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(182,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[181])).
% 0.21/0.58 tff(183,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.21/0.58 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.58 tff(184,plain,
% 0.21/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(185,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[184])).
% 0.21/0.58 tff(186,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(187,plain,
% 0.21/0.58 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(188,plain,
% 0.21/0.58 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[187])).
% 0.21/0.58 tff(189,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.21/0.58 tff(190,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.58 tff(191,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.21/0.58 tff(192,plain,(
% 0.21/0.58 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(skolemize,[status(sab)],[191])).
% 0.21/0.58 tff(193,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.21/0.58 tff(194,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[193, 183])).
% 0.21/0.58 tff(195,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[194, 178])).
% 0.21/0.58 tff(196,plain,
% 0.21/0.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(197,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(198,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.58 tff(199,plain,
% 0.21/0.58 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[198, 45, 44, 23, 195])).
% 0.21/0.58 tff(200,plain,
% 0.21/0.58 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(201,plain,
% 0.21/0.58 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(202,plain,
% 0.21/0.58 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.21/0.58 tff(203,plain,
% 0.21/0.58 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[202, 199, 176])).
% 0.21/0.58 tff(204,plain,
% 0.21/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(205,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.58 tff(206,plain,
% 0.21/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(207,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[206])).
% 0.21/0.58 tff(208,plain,
% 0.21/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(209,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[208])).
% 0.21/0.58 tff(210,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.21/0.58 inference(transitivity,[status(thm)],[209, 207])).
% 0.21/0.58 tff(211,plain,
% 0.21/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(212,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[211])).
% 0.21/0.58 tff(213,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(214,plain,
% 0.21/0.58 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(215,plain,
% 0.21/0.58 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[214])).
% 0.21/0.58 tff(216,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_filter_2')).
% 0.21/0.58 tff(217,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.21/0.58 tff(218,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.21/0.58 tff(219,plain,(
% 0.21/0.58 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(skolemize,[status(sab)],[218])).
% 0.21/0.58 tff(220,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.21/0.58 tff(221,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[220, 210])).
% 0.21/0.58 tff(222,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[221, 205])).
% 0.21/0.58 tff(223,plain,
% 0.21/0.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(224,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(225,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.21/0.58 tff(226,plain,
% 0.21/0.58 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[225, 45, 44, 23, 222])).
% 0.21/0.58 tff(227,plain,
% 0.21/0.58 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(228,plain,
% 0.21/0.58 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(229,plain,
% 0.21/0.58 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.21/0.58 tff(230,plain,
% 0.21/0.58 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[229, 226])).
% 0.21/0.58 tff(231,plain,
% 0.21/0.58 (k7_filter_2(A!0, B!1) = B!1),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[230, 203])).
% 0.21/0.58 tff(232,plain,
% 0.21/0.58 (^[A: $i] : refl((v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(233,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[232])).
% 0.21/0.58 tff(234,plain,
% 0.21/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(235,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[234])).
% 0.21/0.58 tff(236,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(237,plain,
% 0.21/0.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(238,plain,
% 0.21/0.58 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[237])).
% 0.21/0.58 tff(239,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t78_lattice2')).
% 0.21/0.58 tff(240,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.21/0.58 tff(241,plain,
% 0.21/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[240, 236])).
% 0.21/0.58 tff(242,plain,(
% 0.21/0.58 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.21/0.58 inference(skolemize,[status(sab)],[241])).
% 0.21/0.58 tff(243,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[242, 235])).
% 0.21/0.58 tff(244,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[243, 233])).
% 0.21/0.58 tff(245,plain,
% 0.21/0.58 (v13_lattices(A!0)),
% 0.21/0.58 inference(or_elim,[status(thm)],[118])).
% 0.21/0.58 tff(246,plain,
% 0.21/0.58 (((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | ((~v13_lattices(A!0)) | v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~v13_lattices(A!0)) | v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(247,plain,
% 0.21/0.58 ((v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0))) <=> ((~v13_lattices(A!0)) | v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(248,plain,
% 0.21/0.58 (((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | ((~v13_lattices(A!0)) | v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[247])).
% 0.21/0.58 tff(249,plain,
% 0.21/0.58 (((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~v13_lattices(A!0)) | v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.21/0.58 inference(transitivity,[status(thm)],[248, 246])).
% 0.21/0.58 tff(250,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(251,plain,
% 0.21/0.58 ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~v13_lattices(A!0)) | v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.58 tff(252,plain,
% 0.21/0.58 (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[251, 45, 44, 23, 245, 244])).
% 0.21/0.58 tff(253,plain,
% 0.21/0.58 (k6_lattices(k1_lattice2(A!0)) = k5_lattices(A!0)),
% 0.21/0.58 inference(symmetry,[status(thm)],[252])).
% 0.21/0.58 tff(254,plain,
% 0.21/0.58 (k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k6_lattices(k1_lattice2(A!0))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.58 tff(255,plain,
% 0.21/0.58 (k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k5_lattices(A!0)),
% 0.21/0.58 inference(transitivity,[status(thm)],[254, 253])).
% 0.21/0.58 tff(256,plain,
% 0.21/0.58 (r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) <=> r2_hidden(k5_lattices(A!0), B!1)),
% 0.21/0.58 inference(monotonicity,[status(thm)],[255, 231])).
% 0.21/0.58 tff(257,plain,
% 0.21/0.58 (r2_hidden(k5_lattices(A!0), B!1) <=> r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1))),
% 0.21/0.58 inference(symmetry,[status(thm)],[256])).
% 0.21/0.58 tff(258,plain,
% 0.21/0.58 ((~r2_hidden(k5_lattices(A!0), B!1)) <=> (~r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[257])).
% 0.21/0.58 tff(259,plain,
% 0.21/0.58 (~r2_hidden(k5_lattices(A!0), B!1)),
% 0.21/0.58 inference(or_elim,[status(thm)],[118])).
% 0.21/0.58 tff(260,plain,
% 0.21/0.58 (~r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.21/0.58 tff(261,plain,
% 0.21/0.58 (v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v14_lattices(k1_lattice2(A!0))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.58 tff(262,plain,
% 0.21/0.58 (v14_lattices(k1_lattice2(A!0)) <=> v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.58 inference(symmetry,[status(thm)],[261])).
% 0.21/0.58 tff(263,plain,
% 0.21/0.58 (^[A: $i] : refl((v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(264,plain,
% 0.21/0.58 (![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[263])).
% 0.21/0.59 tff(265,plain,
% 0.21/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(266,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[265])).
% 0.21/0.59 tff(267,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(268,plain,
% 0.21/0.59 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(269,plain,
% 0.21/0.59 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[268])).
% 0.21/0.59 tff(270,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_lattice2')).
% 0.21/0.59 tff(271,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.21/0.59 tff(272,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.21/0.59 tff(273,plain,(
% 0.21/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.21/0.59 inference(skolemize,[status(sab)],[272])).
% 0.21/0.59 tff(274,plain,
% 0.21/0.59 (![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.21/0.59 tff(275,plain,
% 0.21/0.59 (![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[274, 264])).
% 0.21/0.59 tff(276,plain,
% 0.21/0.59 (((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(277,plain,
% 0.21/0.59 ((v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(278,plain,
% 0.21/0.59 (((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))))),
% 0.21/0.59 inference(monotonicity,[status(thm)],[277])).
% 0.21/0.59 tff(279,plain,
% 0.21/0.59 (((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))),
% 0.21/0.59 inference(transitivity,[status(thm)],[278, 276])).
% 0.21/0.59 tff(280,plain,
% 0.21/0.59 ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(281,plain,
% 0.21/0.59 ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.21/0.59 tff(282,plain,
% 0.21/0.59 (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[281, 45, 44, 23, 275])).
% 0.21/0.59 tff(283,plain,
% 0.21/0.59 ((~(v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))) | (~v13_lattices(A!0)) | v14_lattices(k1_lattice2(A!0))),
% 0.21/0.59 inference(tautology,[status(thm)],[])).
% 0.21/0.59 tff(284,plain,
% 0.21/0.59 ((~(v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))) | v14_lattices(k1_lattice2(A!0))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[283, 245])).
% 0.21/0.59 tff(285,plain,
% 0.21/0.59 (v14_lattices(k1_lattice2(A!0))),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[284, 282])).
% 0.21/0.59 tff(286,plain,
% 0.21/0.59 (v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[285, 262])).
% 0.21/0.59 tff(287,plain,
% 0.21/0.59 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(288,plain,
% 0.21/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[287])).
% 0.21/0.59 tff(289,plain,
% 0.21/0.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(290,plain,
% 0.21/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[289])).
% 0.21/0.59 tff(291,plain,
% 0.21/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))),
% 0.21/0.59 inference(transitivity,[status(thm)],[290, 288])).
% 0.21/0.59 tff(292,plain,
% 0.21/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))), ((r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))))), rewrite((r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))), ((r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))))), (![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(293,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[292])).
% 0.21/0.59 tff(294,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(295,plain,
% 0.21/0.59 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | r2_hidden(k6_lattices(A), B))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | r2_hidden(k6_lattices(A), B)))), ((m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B))) <=> (m1_filter_0(B, A) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | r2_hidden(k6_lattices(A), B))))), rewrite((m1_filter_0(B, A) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | r2_hidden(k6_lattices(A), B))) <=> (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))), ((m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B))) <=> (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))))), (![B: $i] : (m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B))) <=> ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(296,plain,
% 0.21/0.59 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[295])).
% 0.21/0.59 tff(297,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => r2_hidden(k6_lattices(A), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_filter_0')).
% 0.21/0.59 tff(298,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.21/0.59 tff(299,plain,
% 0.21/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))),
% 0.45/0.59 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.45/0.59 tff(300,plain,(
% 0.45/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))))),
% 0.45/0.59 inference(skolemize,[status(sab)],[299])).
% 0.45/0.59 tff(301,plain,
% 0.45/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))),
% 0.45/0.59 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.45/0.59 tff(302,plain,
% 0.45/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_lattices(A))))),
% 0.45/0.59 inference(modus_ponens,[status(thm)],[301, 291])).
% 0.45/0.59 tff(303,plain,
% 0.45/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.45/0.59 inference(rewrite,[status(thm)],[])).
% 0.45/0.59 tff(304,plain,
% 0.45/0.59 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.45/0.59 inference(rewrite,[status(thm)],[])).
% 0.45/0.59 tff(305,plain,
% 0.45/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.45/0.59 inference(monotonicity,[status(thm)],[304])).
% 0.45/0.59 tff(306,plain,
% 0.45/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.45/0.59 inference(transitivity,[status(thm)],[305, 303])).
% 0.45/0.59 tff(307,plain,
% 0.45/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.45/0.59 inference(quant_inst,[status(thm)],[])).
% 0.45/0.59 tff(308,plain,
% 0.45/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | r2_hidden(k6_lattices(A), B) | (~m1_filter_0(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~v14_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.45/0.59 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.45/0.59 tff(309,plain,
% 0.45/0.59 (![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.45/0.59 inference(unit_resolution,[status(thm)],[308, 302, 79, 58, 52])).
% 0.45/0.59 tff(310,plain,
% 0.45/0.59 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(311,plain,
% 0.45/0.60 (((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.45/0.60 inference(rewrite,[status(thm)],[])).
% 0.45/0.60 tff(312,plain,
% 0.45/0.60 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.45/0.60 inference(monotonicity,[status(thm)],[311])).
% 0.45/0.60 tff(313,plain,
% 0.45/0.60 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.45/0.60 inference(transitivity,[status(thm)],[312, 310])).
% 0.45/0.60 tff(314,plain,
% 0.45/0.60 ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.45/0.60 inference(quant_inst,[status(thm)],[])).
% 0.45/0.60 tff(315,plain,
% 0.45/0.60 ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B) | (~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | r2_hidden(k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1)) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.45/0.60 inference(modus_ponens,[status(thm)],[314, 313])).
% 0.45/0.60 tff(316,plain,
% 0.45/0.60 (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[315, 79, 58, 52, 309, 286, 260])).
% 0.45/0.60 tff(317,plain,
% 0.45/0.60 ((~(m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.45/0.60 inference(tautology,[status(thm)],[])).
% 0.45/0.60 tff(318,plain,
% 0.45/0.60 ($false),
% 0.45/0.60 inference(unit_resolution,[status(thm)],[317, 316, 150, 104])).
% 0.45/0.60 % SZS output end Proof
% 0.45/0.60 % E exiting
%------------------------------------------------------------------------------