%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT317+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:14:19 AM UTC 2025
% Result : Theorem 70.74s 70.92s
% Output : Proof 71.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT317+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 20:14:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 70.74/70.92 % SZS status Theorem
% 70.74/70.92 % SZS output start Proof
% 70.74/70.92 tff(r1_tarski_type, type, (
% 70.74/70.92 r1_tarski: ( $i * $i ) > $o)).
% 70.74/70.92 tff(k20_filter_2_type, type, (
% 70.74/70.92 k20_filter_2: ( $i * $i * $i ) > $i)).
% 70.74/70.92 tff(tptp_fun_C_2_type, type, (
% 70.74/70.92 tptp_fun_C_2: $i)).
% 70.74/70.92 tff(tptp_fun_B_1_type, type, (
% 70.74/70.92 tptp_fun_B_1: $i)).
% 70.74/70.92 tff(tptp_fun_A_0_type, type, (
% 70.74/70.92 tptp_fun_A_0: $i)).
% 70.74/70.92 tff(k5_filter_0_type, type, (
% 70.74/70.92 k5_filter_0: ( $i * $i * $i ) > $i)).
% 70.74/70.92 tff(k7_filter_2_type, type, (
% 70.74/70.92 k7_filter_2: ( $i * $i ) > $i)).
% 70.74/70.92 tff(g3_lattices_type, type, (
% 70.74/70.92 g3_lattices: ( $i * $i * $i ) > $i)).
% 70.74/70.92 tff(u2_lattices_type, type, (
% 70.74/70.92 u2_lattices: $i > $i)).
% 70.74/70.92 tff(u1_lattices_type, type, (
% 70.74/70.92 u1_lattices: $i > $i)).
% 70.74/70.92 tff(u1_struct_0_type, type, (
% 70.74/70.92 u1_struct_0: $i > $i)).
% 70.74/70.92 tff(k8_filter_2_type, type, (
% 70.74/70.92 k8_filter_2: ( $i * $i ) > $i)).
% 70.74/70.92 tff(m1_subset_1_type, type, (
% 70.74/70.92 m1_subset_1: ( $i * $i ) > $o)).
% 70.74/70.92 tff(k1_zfmisc_1_type, type, (
% 70.74/70.92 k1_zfmisc_1: $i > $i)).
% 70.74/70.92 tff(m2_lattice4_type, type, (
% 70.74/70.92 m2_lattice4: ( $i * $i ) > $o)).
% 70.74/70.92 tff(v1_xboole_0_type, type, (
% 70.74/70.92 v1_xboole_0: $i > $o)).
% 70.74/70.92 tff(m2_filter_2_type, type, (
% 70.74/70.92 m2_filter_2: ( $i * $i ) > $o)).
% 70.74/70.92 tff(v10_lattices_type, type, (
% 70.74/70.92 v10_lattices: $i > $o)).
% 70.74/70.92 tff(l3_lattices_type, type, (
% 70.74/70.92 l3_lattices: $i > $o)).
% 70.74/70.92 tff(v3_struct_0_type, type, (
% 70.74/70.92 v3_struct_0: $i > $o)).
% 70.74/70.92 tff(k1_lattice2_type, type, (
% 70.74/70.92 k1_lattice2: $i > $i)).
% 70.74/70.92 tff(tptp_fun_B_7_type, type, (
% 70.74/70.92 tptp_fun_B_7: $i > $i)).
% 70.74/70.92 tff(tptp_fun_B_19_type, type, (
% 70.74/70.92 tptp_fun_B_19: $i > $i)).
% 70.74/70.92 tff(m1_filter_0_type, type, (
% 70.74/70.92 m1_filter_0: ( $i * $i ) > $o)).
% 70.74/70.92 tff(m1_filter_2_type, type, (
% 70.74/70.92 m1_filter_2: ( $i * $i ) > $o)).
% 70.74/70.92 tff(v9_lattices_type, type, (
% 70.74/70.92 v9_lattices: $i > $o)).
% 70.74/70.92 tff(v8_lattices_type, type, (
% 70.74/70.92 v8_lattices: $i > $o)).
% 70.74/70.92 tff(v7_lattices_type, type, (
% 70.74/70.92 v7_lattices: $i > $o)).
% 70.74/70.92 tff(v6_lattices_type, type, (
% 70.74/70.92 v6_lattices: $i > $o)).
% 70.74/70.92 tff(v5_lattices_type, type, (
% 70.74/70.92 v5_lattices: $i > $o)).
% 70.74/70.92 tff(v4_lattices_type, type, (
% 70.74/70.92 v4_lattices: $i > $o)).
% 70.74/70.92 tff(v3_lattices_type, type, (
% 70.74/70.92 v3_lattices: $i > $o)).
% 70.74/70.92 tff(k15_filter_2_type, type, (
% 70.74/70.92 k15_filter_2: ( $i * $i ) > $i)).
% 70.74/70.92 tff(1,plain,
% 70.74/70.92 (^[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)))))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(2,plain,
% 70.74/70.92 (![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))))))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[1])).
% 70.74/70.92 tff(3,plain,
% 70.74/70.92 (^[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)))))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(4,plain,
% 70.74/70.92 (![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))))))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[3])).
% 70.74/70.92 tff(5,plain,
% 70.74/70.92 (![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))))))),
% 70.74/70.92 inference(transitivity,[status(thm)],[4, 2])).
% 70.74/70.92 tff(6,plain,
% 70.74/70.92 (^[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))))))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(7,plain,
% 70.74/70.92 (![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))))))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[6])).
% 70.74/70.92 tff(8,plain,
% 70.74/70.92 (![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))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(9,plain,
% 70.74/70.92 (^[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))))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(10,plain,
% 70.74/70.92 (![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))))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[9])).
% 70.74/70.92 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 70.74/70.92 tff(12,plain,
% 70.74/70.92 (![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))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[11, 10])).
% 70.74/70.92 tff(13,plain,
% 70.74/70.92 (![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))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[12, 8])).
% 70.74/70.92 tff(14,plain,(
% 70.74/70.92 ![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))))),
% 70.74/70.92 inference(skolemize,[status(sab)],[13])).
% 70.74/70.92 tff(15,plain,
% 70.74/70.92 (![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))))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[14, 7])).
% 70.74/70.92 tff(16,plain,
% 70.74/70.92 (![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))))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[15, 5])).
% 70.74/70.92 tff(17,plain,
% 70.74/70.92 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m2_filter_2(B!1, A!0) & (~((~m2_filter_2(C!2, A!0)) | (r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & (~((~m2_filter_2(C!2, A!0)) | (r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(18,plain,
% 70.74/70.92 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C)))))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(19,plain,
% 70.74/70.92 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ![C: $i] : (m2_filter_2(C, A) => (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C)))))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(20,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ![C: $i] : (m2_filter_2(C, A) => (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t51_filter_2')).
% 70.74/70.92 tff(21,plain,
% 70.74/70.92 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[20, 19])).
% 70.74/70.92 tff(22,plain,
% 70.74/70.92 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[21, 18])).
% 70.74/70.92 tff(23,plain,
% 70.74/70.92 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[22, 18])).
% 70.74/70.92 tff(24,plain,
% 70.74/70.92 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | (r1_tarski(B, k20_filter_2(A, B, C)) & r1_tarski(C, k20_filter_2(A, B, C))))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[23, 18])).
% 70.74/70.92 tff(25,plain,
% 70.74/70.92 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & (~((~m2_filter_2(C!2, A!0)) | (r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[24, 17])).
% 70.74/70.92 tff(26,plain,
% 70.74/70.92 (l3_lattices(A!0)),
% 70.74/70.92 inference(and_elim,[status(thm)],[25])).
% 70.74/70.92 tff(27,plain,
% 70.74/70.92 (v10_lattices(A!0)),
% 70.74/70.92 inference(and_elim,[status(thm)],[25])).
% 70.74/70.92 tff(28,plain,
% 70.74/70.92 (~v3_struct_0(A!0)),
% 70.74/70.92 inference(and_elim,[status(thm)],[25])).
% 70.74/70.92 tff(29,plain,
% 70.74/70.92 (((~![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))))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(30,plain,
% 70.74/70.92 ((~![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))))))),
% 70.74/70.92 inference(quant_inst,[status(thm)],[])).
% 70.74/70.92 tff(31,plain,
% 70.74/70.92 ((~![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)))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[30, 29])).
% 70.74/70.92 tff(32,plain,
% 70.74/70.92 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 70.74/70.92 inference(unit_resolution,[status(thm)],[31, 28, 27, 26, 16])).
% 70.74/70.92 tff(33,plain,
% 70.74/70.92 (~((~m2_filter_2(C!2, A!0)) | (r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))))),
% 70.74/70.92 inference(and_elim,[status(thm)],[25])).
% 70.74/70.92 tff(34,plain,
% 70.74/70.92 (m2_filter_2(C!2, A!0)),
% 70.74/70.92 inference(or_elim,[status(thm)],[33])).
% 70.74/70.92 tff(35,plain,
% 70.74/70.92 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(36,plain,
% 70.74/70.92 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 70.74/70.92 inference(quant_inst,[status(thm)],[])).
% 70.74/70.92 tff(37,plain,
% 70.74/70.92 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[36, 35])).
% 70.74/70.92 tff(38,plain,
% 70.74/70.92 (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))),
% 70.74/70.92 inference(unit_resolution,[status(thm)],[37, 34, 32])).
% 70.74/70.92 tff(39,plain,
% 70.74/70.92 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | m2_lattice4(C!2, A!0)),
% 70.74/70.92 inference(tautology,[status(thm)],[])).
% 70.74/70.92 tff(40,plain,
% 70.74/70.92 (m2_lattice4(C!2, A!0)),
% 70.74/70.92 inference(unit_resolution,[status(thm)],[39, 38])).
% 70.74/70.92 tff(41,plain,
% 70.74/70.92 (^[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))))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(42,plain,
% 70.74/70.92 (![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)))))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[41])).
% 70.74/70.92 tff(43,plain,
% 70.74/70.92 (^[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))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(44,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[43])).
% 70.74/70.92 tff(45,plain,
% 70.74/70.92 (^[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))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(46,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[45])).
% 70.74/70.92 tff(47,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(transitivity,[status(thm)],[46, 44])).
% 70.74/70.92 tff(48,plain,
% 70.74/70.92 (^[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)))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(49,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[48])).
% 70.74/70.92 tff(50,plain,
% 70.74/70.92 (![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)))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(51,plain,
% 70.74/70.92 (^[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)))))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(52,plain,
% 70.74/70.92 (![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)))))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[51])).
% 70.74/70.92 tff(53,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 70.74/70.92 tff(54,plain,
% 70.74/70.92 (![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)))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[53, 52])).
% 70.74/70.92 tff(55,plain,
% 70.74/70.92 (![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)))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[54, 50])).
% 70.74/70.92 tff(56,plain,(
% 70.74/70.92 ![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)))))),
% 70.74/70.92 inference(skolemize,[status(sab)],[55])).
% 70.74/70.92 tff(57,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[56, 49])).
% 70.74/70.92 tff(58,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[57, 47])).
% 70.74/70.92 tff(59,plain,
% 70.74/70.92 (![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)))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[58, 42])).
% 70.74/70.92 tff(60,plain,
% 70.74/70.92 (((~![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)))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(61,plain,
% 70.74/70.92 ((~![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)))))),
% 70.74/70.92 inference(quant_inst,[status(thm)],[])).
% 70.74/70.92 tff(62,plain,
% 70.74/70.92 ((~![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))))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[61, 60])).
% 70.74/70.92 tff(63,plain,
% 70.74/70.92 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 70.74/70.92 inference(unit_resolution,[status(thm)],[62, 28, 27, 26, 59])).
% 70.74/70.92 tff(64,plain,
% 70.74/70.92 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, 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(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 70.74/70.92 inference(rewrite,[status(thm)],[])).
% 70.74/70.92 tff(65,plain,
% 70.74/70.92 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 70.74/70.92 inference(quant_inst,[status(thm)],[])).
% 70.74/70.92 tff(66,plain,
% 70.74/70.92 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.92 inference(modus_ponens,[status(thm)],[65, 64])).
% 70.74/70.92 tff(67,plain,
% 70.74/70.92 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.92 inference(unit_resolution,[status(thm)],[66, 63, 40])).
% 70.74/70.92 tff(68,plain,
% 70.74/70.92 (^[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))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(69,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[68])).
% 70.74/70.92 tff(70,plain,
% 70.74/70.92 (^[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))))),
% 70.74/70.92 inference(bind,[status(th)],[])).
% 70.74/70.92 tff(71,plain,
% 70.74/70.92 (![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)))),
% 70.74/70.92 inference(quant_intro,[status(thm)],[70])).
% 70.74/70.92 tff(72,plain,
% 70.74/70.92 (^[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))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(73,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[72])).
% 70.74/70.93 tff(74,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(transitivity,[status(thm)],[73, 71])).
% 70.74/70.93 tff(75,plain,
% 70.74/70.93 (^[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)))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(76,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[75])).
% 70.74/70.93 tff(77,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(78,plain,
% 70.74/70.93 (^[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)))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(79,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[78])).
% 70.74/70.93 tff(80,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_filter_2')).
% 70.74/70.93 tff(81,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[80, 79])).
% 70.74/70.93 tff(82,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[81, 77])).
% 70.74/70.93 tff(83,plain,(
% 70.74/70.93 ![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)))),
% 70.74/70.93 inference(skolemize,[status(sab)],[82])).
% 70.74/70.93 tff(84,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[83, 76])).
% 70.74/70.93 tff(85,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[84, 74])).
% 70.74/70.93 tff(86,plain,
% 70.74/70.93 (![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)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[85, 69])).
% 70.74/70.93 tff(87,plain,
% 70.74/70.93 (((~![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)))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(88,plain,
% 70.74/70.93 ((~![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)))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(89,plain,
% 70.74/70.93 ((~![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))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[88, 87])).
% 70.74/70.93 tff(90,plain,
% 70.74/70.93 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[89, 28, 27, 26, 86])).
% 70.74/70.93 tff(91,plain,
% 70.74/70.93 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(92,plain,
% 70.74/70.93 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(93,plain,
% 70.74/70.93 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2)),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[92, 91])).
% 70.74/70.93 tff(94,plain,
% 70.74/70.93 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2)),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[93, 90])).
% 70.74/70.93 tff(95,plain,
% 70.74/70.93 (k7_filter_2(A!0, C!2) = C!2),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[94, 67])).
% 70.74/70.93 tff(96,plain,
% 70.74/70.93 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(97,plain,
% 70.74/70.93 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[96])).
% 70.74/70.93 tff(98,plain,
% 70.74/70.93 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(99,plain,
% 70.74/70.93 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[98])).
% 70.74/70.93 tff(100,plain,
% 70.74/70.93 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(101,plain,
% 70.74/70.93 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(102,plain,
% 70.74/70.93 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[101])).
% 70.74/70.93 tff(103,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_filter_2')).
% 70.74/70.93 tff(104,plain,
% 70.74/70.93 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[103, 102])).
% 70.74/70.93 tff(105,plain,
% 70.74/70.93 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[104, 100])).
% 70.74/70.93 tff(106,plain,(
% 70.74/70.93 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 70.74/70.93 inference(skolemize,[status(sab)],[105])).
% 70.74/70.93 tff(107,plain,
% 70.74/70.93 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[106, 99])).
% 70.74/70.93 tff(108,plain,
% 70.74/70.93 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[107, 97])).
% 70.74/70.93 tff(109,plain,
% 70.74/70.93 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(110,plain,
% 70.74/70.93 ((v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(111,plain,
% 70.74/70.93 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))))),
% 70.74/70.93 inference(monotonicity,[status(thm)],[110])).
% 70.74/70.93 tff(112,plain,
% 70.74/70.93 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 70.74/70.93 inference(transitivity,[status(thm)],[111, 109])).
% 70.74/70.93 tff(113,plain,
% 70.74/70.93 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(114,plain,
% 70.74/70.93 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[113, 112])).
% 70.74/70.93 tff(115,plain,
% 70.74/70.93 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[114, 28, 27, 26, 108])).
% 70.74/70.93 tff(116,plain,
% 70.74/70.93 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[115, 67])).
% 70.74/70.93 tff(117,plain,
% 70.74/70.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(118,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[117])).
% 70.74/70.93 tff(119,plain,
% 70.74/70.93 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(120,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[119])).
% 70.74/70.93 tff(121,plain,
% 70.74/70.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(122,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[121])).
% 70.74/70.93 tff(123,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 70.74/70.93 inference(transitivity,[status(thm)],[122, 120])).
% 70.74/70.93 tff(124,plain,
% 70.74/70.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(125,plain,
% 70.74/70.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[124])).
% 70.74/70.93 tff(126,plain,
% 70.74/70.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(127,plain,
% 70.74/70.93 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(128,plain,
% 70.74/70.93 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[127])).
% 70.74/70.93 tff(129,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_filter_2')).
% 70.74/70.93 tff(130,plain,
% 70.74/70.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[129, 128])).
% 70.74/70.93 tff(131,plain,
% 70.74/70.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[130, 126])).
% 70.74/70.93 tff(132,plain,(
% 70.74/70.93 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(skolemize,[status(sab)],[131])).
% 70.74/70.93 tff(133,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[132, 125])).
% 70.74/70.93 tff(134,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[133, 123])).
% 70.74/70.93 tff(135,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[134, 118])).
% 70.74/70.93 tff(136,plain,
% 70.74/70.93 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(137,plain,
% 70.74/70.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(138,plain,
% 70.74/70.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[137, 136])).
% 70.74/70.93 tff(139,plain,
% 70.74/70.93 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[138, 28, 27, 26, 135])).
% 70.74/70.93 tff(140,plain,
% 70.74/70.93 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(141,plain,
% 70.74/70.93 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(142,plain,
% 70.74/70.93 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[141, 140])).
% 70.74/70.93 tff(143,plain,
% 70.74/70.93 (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[142, 139, 116])).
% 70.74/70.93 tff(144,plain,
% 70.74/70.93 (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = C!2),
% 70.74/70.93 inference(transitivity,[status(thm)],[143, 95])).
% 70.74/70.93 tff(145,plain,
% 70.74/70.93 (m2_filter_2(B!1, A!0)),
% 70.74/70.93 inference(and_elim,[status(thm)],[25])).
% 70.74/70.93 tff(146,plain,
% 70.74/70.93 (((~![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)))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(147,plain,
% 70.74/70.93 ((~![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)))))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(148,plain,
% 70.74/70.93 ((~![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))))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[147, 146])).
% 70.74/70.93 tff(149,plain,
% 70.74/70.93 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[148, 145, 32])).
% 70.74/70.93 tff(150,plain,
% 70.74/70.93 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 70.74/70.93 inference(tautology,[status(thm)],[])).
% 70.74/70.93 tff(151,plain,
% 70.74/70.93 (m2_lattice4(B!1, A!0)),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[150, 149])).
% 70.74/70.93 tff(152,plain,
% 70.74/70.93 (((~![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))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(153,plain,
% 70.74/70.93 ((~![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))))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(154,plain,
% 70.74/70.93 ((~![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)))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[153, 152])).
% 70.74/70.93 tff(155,plain,
% 70.74/70.93 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[154, 63, 151])).
% 70.74/70.93 tff(156,plain,
% 70.74/70.93 (((~![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))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(157,plain,
% 70.74/70.93 ((~![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))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(158,plain,
% 70.74/70.93 ((~![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)),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[157, 156])).
% 70.74/70.93 tff(159,plain,
% 70.74/70.93 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[158, 90])).
% 70.74/70.93 tff(160,plain,
% 70.74/70.93 (k7_filter_2(A!0, B!1) = B!1),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[159, 155])).
% 70.74/70.93 tff(161,plain,
% 70.74/70.93 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(162,plain,
% 70.74/70.93 ((v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(163,plain,
% 70.74/70.93 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))))),
% 70.74/70.93 inference(monotonicity,[status(thm)],[162])).
% 70.74/70.93 tff(164,plain,
% 70.74/70.93 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 70.74/70.93 inference(transitivity,[status(thm)],[163, 161])).
% 70.74/70.93 tff(165,plain,
% 70.74/70.93 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(166,plain,
% 70.74/70.93 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[165, 164])).
% 70.74/70.93 tff(167,plain,
% 70.74/70.93 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[166, 28, 27, 26, 108])).
% 70.74/70.93 tff(168,plain,
% 70.74/70.93 (m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[167, 155])).
% 70.74/70.93 tff(169,plain,
% 70.74/70.93 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)))),
% 70.74/70.93 inference(rewrite,[status(thm)],[])).
% 70.74/70.93 tff(170,plain,
% 70.74/70.93 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)))),
% 70.74/70.93 inference(quant_inst,[status(thm)],[])).
% 70.74/70.93 tff(171,plain,
% 70.74/70.93 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1))),
% 70.74/70.93 inference(modus_ponens,[status(thm)],[170, 169])).
% 70.74/70.93 tff(172,plain,
% 70.74/70.93 (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)),
% 70.74/70.93 inference(unit_resolution,[status(thm)],[171, 139, 168])).
% 70.74/70.93 tff(173,plain,
% 70.74/70.93 (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = B!1),
% 70.74/70.93 inference(transitivity,[status(thm)],[172, 160])).
% 70.74/70.93 tff(174,plain,
% 70.74/70.93 (k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k20_filter_2(A!0, B!1, C!2)),
% 70.74/70.93 inference(monotonicity,[status(thm)],[173, 144])).
% 70.74/70.93 tff(175,plain,
% 70.74/70.93 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(176,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[175])).
% 70.74/70.93 tff(177,plain,
% 70.74/70.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(178,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[177])).
% 70.74/70.93 tff(179,plain,
% 70.74/70.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.93 inference(transitivity,[status(thm)],[178, 176])).
% 70.74/70.93 tff(180,plain,
% 70.74/70.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 70.74/70.93 inference(bind,[status(th)],[])).
% 70.74/70.93 tff(181,plain,
% 70.74/70.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.93 inference(quant_intro,[status(thm)],[180])).
% 70.74/70.93 tff(182,plain,
% 70.74/70.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(183,plain,
% 70.74/70.94 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(184,plain,
% 70.74/70.94 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[183])).
% 70.74/70.94 tff(185,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 70.74/70.94 tff(186,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[185, 184])).
% 70.74/70.94 tff(187,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[186, 182])).
% 70.74/70.94 tff(188,plain,(
% 70.74/70.94 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.94 inference(skolemize,[status(sab)],[187])).
% 70.74/70.94 tff(189,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[188, 181])).
% 70.74/70.94 tff(190,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[189, 179])).
% 70.74/70.94 tff(191,plain,
% 70.74/70.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~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] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~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] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(192,plain,
% 70.74/70.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 70.74/70.94 inference(quant_inst,[status(thm)],[])).
% 70.74/70.94 tff(193,plain,
% 70.74/70.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[192, 191])).
% 70.74/70.94 tff(194,plain,
% 70.74/70.94 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[193, 28, 27, 26, 190])).
% 70.74/70.94 tff(195,plain,
% 70.74/70.94 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(196,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[195])).
% 70.74/70.94 tff(197,plain,
% 70.74/70.94 (^[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))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(198,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[197])).
% 70.74/70.94 tff(199,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(200,plain,
% 70.74/70.94 (^[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_0(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, 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)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(201,plain,
% 70.74/70.94 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[200])).
% 70.74/70.94 tff(202,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','existence_m1_filter_0')).
% 70.74/70.94 tff(203,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[202, 201])).
% 70.74/70.94 tff(204,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[203, 199])).
% 70.74/70.94 tff(205,plain,(
% 70.74/70.94 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A))),
% 70.74/70.94 inference(skolemize,[status(sab)],[204])).
% 70.74/70.94 tff(206,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[205, 198])).
% 70.74/70.94 tff(207,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[206, 196])).
% 70.74/70.94 tff(208,plain,
% 70.74/70.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(209,plain,
% 70.74/70.94 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(210,plain,
% 70.74/70.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0)))),
% 70.74/70.94 inference(monotonicity,[status(thm)],[209])).
% 70.74/70.94 tff(211,plain,
% 70.74/70.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 70.74/70.94 inference(transitivity,[status(thm)],[210, 208])).
% 70.74/70.94 tff(212,plain,
% 70.74/70.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0)))),
% 70.74/70.94 inference(quant_inst,[status(thm)],[])).
% 70.74/70.94 tff(213,plain,
% 70.74/70.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0)),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[212, 211])).
% 70.74/70.94 tff(214,plain,
% 70.74/70.94 (m1_filter_0(tptp_fun_B_7(A!0), A!0)),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[213, 28, 27, 26, 207])).
% 70.74/70.94 tff(215,plain,
% 70.74/70.94 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(216,plain,
% 70.74/70.94 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 70.74/70.94 inference(quant_inst,[status(thm)],[])).
% 70.74/70.94 tff(217,plain,
% 70.74/70.94 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[216, 215])).
% 70.74/70.94 tff(218,plain,
% 70.74/70.94 (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[217, 214, 194])).
% 70.74/70.94 tff(219,plain,
% 70.74/70.94 ((v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.94 inference(tautology,[status(thm)],[])).
% 70.74/70.94 tff(220,plain,
% 70.74/70.94 (m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[219, 218])).
% 70.74/70.94 tff(221,plain,
% 70.74/70.94 ((v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | (~v1_xboole_0(tptp_fun_B_7(A!0)))),
% 70.74/70.94 inference(tautology,[status(thm)],[])).
% 70.74/70.94 tff(222,plain,
% 70.74/70.94 (~v1_xboole_0(tptp_fun_B_7(A!0))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[221, 218])).
% 70.74/70.94 tff(223,plain,
% 70.74/70.94 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(224,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[223])).
% 70.74/70.94 tff(225,plain,
% 70.74/70.94 (^[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((m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A)))) <=> (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(226,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[225])).
% 70.74/70.94 tff(227,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(228,plain,
% 70.74/70.94 (^[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] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(229,plain,
% 70.74/70.94 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[228])).
% 70.74/70.94 tff(230,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_lattice4')).
% 70.74/70.94 tff(231,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[230, 229])).
% 70.74/70.94 tff(232,plain,
% 70.74/70.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[231, 227])).
% 70.74/70.94 tff(233,plain,(
% 70.74/70.94 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A)))))),
% 70.74/70.94 inference(skolemize,[status(sab)],[232])).
% 70.74/70.94 tff(234,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[233, 226])).
% 70.74/70.94 tff(235,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[234, 224])).
% 70.74/70.94 tff(236,plain,
% 70.74/70.94 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(237,plain,
% 70.74/70.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))))),
% 70.74/70.94 inference(quant_inst,[status(thm)],[])).
% 70.74/70.94 tff(238,plain,
% 70.74/70.94 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0))))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[237, 236])).
% 70.74/70.94 tff(239,plain,
% 70.74/70.94 (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[238, 28, 27, 26, 235])).
% 70.74/70.94 tff(240,plain,
% 70.74/70.94 ((v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0))) | m2_lattice4(tptp_fun_B_19(A!0), A!0)),
% 70.74/70.94 inference(tautology,[status(thm)],[])).
% 70.74/70.94 tff(241,plain,
% 70.74/70.94 (m2_lattice4(tptp_fun_B_19(A!0), A!0)),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[240, 239])).
% 70.74/70.94 tff(242,plain,
% 70.74/70.94 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), 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(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 70.74/70.94 inference(rewrite,[status(thm)],[])).
% 70.74/70.94 tff(243,plain,
% 70.74/70.94 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 70.74/70.94 inference(quant_inst,[status(thm)],[])).
% 70.74/70.94 tff(244,plain,
% 70.74/70.94 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.94 inference(modus_ponens,[status(thm)],[243, 242])).
% 70.74/70.94 tff(245,plain,
% 70.74/70.94 (m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[244, 241, 63])).
% 70.74/70.94 tff(246,plain,
% 70.74/70.94 ((v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0))) | (~v1_xboole_0(tptp_fun_B_19(A!0)))),
% 70.74/70.94 inference(tautology,[status(thm)],[])).
% 70.74/70.94 tff(247,plain,
% 70.74/70.94 (~v1_xboole_0(tptp_fun_B_19(A!0))),
% 70.74/70.94 inference(unit_resolution,[status(thm)],[246, 239])).
% 70.74/70.94 tff(248,plain,
% 70.74/70.94 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(249,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[248])).
% 70.74/70.94 tff(250,plain,
% 70.74/70.94 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))),
% 70.74/70.94 inference(bind,[status(th)],[])).
% 70.74/70.94 tff(251,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.94 inference(quant_intro,[status(thm)],[250])).
% 70.74/70.94 tff(252,plain,
% 70.74/70.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.94 inference(transitivity,[status(thm)],[251, 249])).
% 70.74/70.94 tff(253,plain,
% 70.74/70.94 (^[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(((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (~(v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (~(~(v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))))), rewrite((~(~(v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (~(v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (~(~(v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))))), rewrite((~(~(v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), rewrite(((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), (((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ((v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), rewrite(((v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), (((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), (((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ((v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), rewrite(((v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), (((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), rewrite(((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), (![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))))),
% 70.74/70.95 inference(bind,[status(th)],[])).
% 70.74/70.95 tff(254,plain,
% 70.74/70.95 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.95 inference(quant_intro,[status(thm)],[253])).
% 70.74/70.95 tff(255,plain,
% 70.74/70.95 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 70.74/70.95 inference(rewrite,[status(thm)],[])).
% 70.74/70.95 tff(256,plain,
% 70.74/70.95 (^[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(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) <=> ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))))), (((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> (((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))), rewrite((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))), (((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))), ((((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), rewrite((((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))), ((((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), (![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), ((((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), rewrite((((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), ((((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), (![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), rewrite((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.95 inference(bind,[status(th)],[])).
% 70.74/70.95 tff(257,plain,
% 70.74/70.95 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 70.74/70.95 inference(quant_intro,[status(thm)],[256])).
% 70.74/70.95 tff(258,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_filter_2')).
% 70.74/70.95 tff(259,plain,
% 70.74/70.95 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 70.74/70.95 inference(modus_ponens,[status(thm)],[258, 257])).
% 70.74/70.95 tff(260,plain,
% 70.74/70.95 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 70.74/70.95 inference(modus_ponens,[status(thm)],[259, 255])).
% 70.74/70.95 tff(261,plain,(
% 70.74/70.95 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 70.74/70.95 inference(skolemize,[status(sab)],[260])).
% 70.74/70.95 tff(262,plain,
% 70.74/70.95 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.95 inference(modus_ponens,[status(thm)],[261, 254])).
% 70.74/70.95 tff(263,plain,
% 70.74/70.95 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 70.74/70.95 inference(modus_ponens,[status(thm)],[262, 252])).
% 70.74/70.95 tff(264,plain,
% 70.74/70.95 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))))),
% 70.74/70.95 inference(rewrite,[status(thm)],[])).
% 70.74/70.95 tff(265,plain,
% 70.74/70.95 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))))),
% 70.74/70.95 inference(quant_inst,[status(thm)],[])).
% 70.74/70.95 tff(266,plain,
% 70.74/70.95 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))),
% 70.74/70.95 inference(modus_ponens,[status(thm)],[265, 264])).
% 70.74/70.95 tff(267,plain,
% 70.74/70.95 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))),
% 70.74/70.95 inference(unit_resolution,[status(thm)],[266, 28, 27, 26, 263])).
% 70.74/70.95 tff(268,plain,
% 70.74/70.95 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))),
% 70.74/70.95 inference(rewrite,[status(thm)],[])).
% 70.74/70.95 tff(269,plain,
% 70.74/70.95 ((v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))) <=> (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))),
% 70.74/70.96 inference(rewrite,[status(thm)],[])).
% 70.74/70.96 tff(270,plain,
% 70.74/70.96 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))))),
% 70.74/70.96 inference(monotonicity,[status(thm)],[269])).
% 70.74/70.96 tff(271,plain,
% 70.74/70.96 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))),
% 70.74/70.96 inference(transitivity,[status(thm)],[270, 268])).
% 70.74/70.96 tff(272,plain,
% 70.74/70.96 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))),
% 70.74/70.96 inference(quant_inst,[status(thm)],[])).
% 70.74/70.96 tff(273,plain,
% 70.74/70.96 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[272, 271])).
% 70.74/70.96 tff(274,plain,
% 70.74/70.96 ((~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))),
% 70.74/70.96 inference(unit_resolution,[status(thm)],[273, 267, 247])).
% 70.74/70.96 tff(275,plain,
% 70.74/70.96 (![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))),
% 70.74/70.96 inference(unit_resolution,[status(thm)],[274, 245])).
% 70.74/70.96 tff(276,plain,
% 70.74/70.96 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | (v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))))),
% 70.74/70.96 inference(rewrite,[status(thm)],[])).
% 70.74/70.96 tff(277,plain,
% 70.74/70.96 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | (v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))))),
% 70.74/70.96 inference(quant_inst,[status(thm)],[])).
% 70.74/70.96 tff(278,plain,
% 70.74/70.96 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[277, 276])).
% 70.74/70.96 tff(279,plain,
% 70.74/70.96 (![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))),
% 70.74/70.96 inference(unit_resolution,[status(thm)],[278, 275, 222, 220])).
% 70.74/70.96 tff(280,plain,
% 70.74/70.96 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | (~v1_xboole_0(B!1))),
% 70.74/70.96 inference(tautology,[status(thm)],[])).
% 70.74/70.96 tff(281,plain,
% 70.74/70.96 (~v1_xboole_0(B!1)),
% 70.74/70.96 inference(unit_resolution,[status(thm)],[280, 149])).
% 70.74/70.96 tff(282,plain,
% 70.74/70.96 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 70.74/70.96 inference(bind,[status(th)],[])).
% 70.74/70.96 tff(283,plain,
% 70.74/70.96 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.96 inference(quant_intro,[status(thm)],[282])).
% 70.74/70.96 tff(284,plain,
% 70.74/70.96 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~v1_xboole_0(k7_filter_2(A, B))) | (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))), rewrite(((~v1_xboole_0(k7_filter_2(A, B))) | (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 70.74/70.96 inference(bind,[status(th)],[])).
% 70.74/70.96 tff(285,plain,
% 70.74/70.96 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.96 inference(quant_intro,[status(thm)],[284])).
% 70.74/70.96 tff(286,plain,
% 70.74/70.96 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.96 inference(rewrite,[status(thm)],[])).
% 70.74/70.96 tff(287,plain,
% 70.74/70.96 (^[A: $i, B: $i] : trans(monotonicity(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)) & (~v1_xboole_0(B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k7_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k7_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k7_filter_2(A, B)))) <=> ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k7_filter_2(A, B)))) <=> ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 70.74/70.96 inference(bind,[status(th)],[])).
% 70.74/70.96 tff(288,plain,
% 70.74/70.96 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k7_filter_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.96 inference(quant_intro,[status(thm)],[287])).
% 70.74/70.96 tff(289,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k7_filter_2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_filter_2')).
% 70.74/70.96 tff(290,plain,
% 70.74/70.96 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[289, 288])).
% 70.74/70.96 tff(291,plain,
% 70.74/70.96 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[290, 286])).
% 70.74/70.96 tff(292,plain,(
% 70.74/70.96 ![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(A, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 70.74/70.96 inference(skolemize,[status(sab)],[291])).
% 70.74/70.96 tff(293,plain,
% 70.74/70.96 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[292, 285])).
% 70.74/70.96 tff(294,plain,
% 70.74/70.96 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[293, 283])).
% 70.74/70.96 tff(295,plain,
% 70.74/70.96 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 70.74/70.96 inference(rewrite,[status(thm)],[])).
% 70.74/70.96 tff(296,plain,
% 70.74/70.96 ((v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 70.74/70.96 inference(rewrite,[status(thm)],[])).
% 70.74/70.96 tff(297,plain,
% 70.74/70.96 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))))),
% 70.74/70.96 inference(monotonicity,[status(thm)],[296])).
% 70.74/70.96 tff(298,plain,
% 70.74/70.96 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 70.74/70.96 inference(transitivity,[status(thm)],[297, 295])).
% 70.74/70.96 tff(299,plain,
% 70.74/70.96 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.74/70.96 inference(quant_inst,[status(thm)],[])).
% 70.74/70.96 tff(300,plain,
% 70.74/70.96 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))),
% 70.74/70.96 inference(modus_ponens,[status(thm)],[299, 298])).
% 70.74/70.96 tff(301,plain,
% 70.74/70.96 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))),
% 70.74/70.96 inference(unit_resolution,[status(thm)],[300, 28, 27, 26, 294])).
% 70.74/70.96 tff(302,plain,
% 70.74/70.96 (~v1_xboole_0(k7_filter_2(A!0, B!1))),
% 70.74/70.96 inference(unit_resolution,[status(thm)],[301, 155, 281])).
% 70.74/70.96 tff(303,plain,
% 70.74/70.96 (((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))) <=> ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))),
% 70.74/70.96 inference(rewrite,[status(thm)],[])).
% 70.74/70.96 tff(304,plain,
% 70.74/70.96 ((v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))) <=> (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))),
% 70.74/70.97 inference(rewrite,[status(thm)],[])).
% 70.74/70.97 tff(305,plain,
% 70.74/70.97 (((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) <=> ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))))),
% 70.74/70.97 inference(monotonicity,[status(thm)],[304])).
% 70.74/70.97 tff(306,plain,
% 70.74/70.97 (((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) <=> ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))),
% 70.74/70.97 inference(transitivity,[status(thm)],[305, 303])).
% 70.74/70.97 tff(307,plain,
% 70.74/70.97 ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))),
% 70.74/70.97 inference(quant_inst,[status(thm)],[])).
% 70.74/70.97 tff(308,plain,
% 70.74/70.97 ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))),
% 70.74/70.97 inference(modus_ponens,[status(thm)],[307, 306])).
% 70.74/70.97 tff(309,plain,
% 70.74/70.97 (![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))),
% 70.74/70.97 inference(unit_resolution,[status(thm)],[308, 168, 302, 279])).
% 70.74/70.97 tff(310,plain,
% 70.74/70.97 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | (~v1_xboole_0(C!2))),
% 70.74/70.97 inference(tautology,[status(thm)],[])).
% 70.74/70.97 tff(311,plain,
% 70.74/70.97 (~v1_xboole_0(C!2)),
% 70.74/70.97 inference(unit_resolution,[status(thm)],[310, 38])).
% 70.74/70.97 tff(312,plain,
% 70.74/70.97 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 70.74/70.97 inference(rewrite,[status(thm)],[])).
% 70.74/70.97 tff(313,plain,
% 70.74/70.97 ((v1_xboole_0(C!2) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 70.74/70.97 inference(rewrite,[status(thm)],[])).
% 70.74/70.97 tff(314,plain,
% 70.74/70.97 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))))),
% 70.74/70.97 inference(monotonicity,[status(thm)],[313])).
% 70.74/70.97 tff(315,plain,
% 70.74/70.97 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 70.74/70.97 inference(transitivity,[status(thm)],[314, 312])).
% 70.74/70.97 tff(316,plain,
% 70.74/70.97 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.74/70.97 inference(quant_inst,[status(thm)],[])).
% 70.74/70.97 tff(317,plain,
% 70.74/70.97 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))),
% 70.74/70.97 inference(modus_ponens,[status(thm)],[316, 315])).
% 70.74/70.97 tff(318,plain,
% 70.74/70.97 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))),
% 70.74/70.97 inference(unit_resolution,[status(thm)],[317, 28, 27, 26, 294])).
% 70.74/70.97 tff(319,plain,
% 70.74/70.97 (~v1_xboole_0(k7_filter_2(A!0, C!2))),
% 70.74/70.97 inference(unit_resolution,[status(thm)],[318, 67, 311])).
% 70.74/70.97 tff(320,plain,
% 70.74/70.97 (((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | (v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))) <=> ((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))),
% 70.74/70.97 inference(rewrite,[status(thm)],[])).
% 70.74/70.97 tff(321,plain,
% 70.74/70.97 ((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | (v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))),
% 70.74/70.97 inference(quant_inst,[status(thm)],[])).
% 70.74/70.97 tff(322,plain,
% 70.74/70.97 ((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))))),
% 70.74/70.97 inference(modus_ponens,[status(thm)],[321, 320])).
% 70.74/70.97 tff(323,plain,
% 70.74/70.97 (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 70.74/70.97 inference(unit_resolution,[status(thm)],[322, 116, 319, 309])).
% 70.74/70.97 tff(324,plain,
% 70.74/70.97 (((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))) | (k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 70.74/70.97 inference(tautology,[status(thm)],[])).
% 70.74/70.97 tff(325,plain,
% 70.74/70.97 (k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))),
% 70.74/70.97 inference(unit_resolution,[status(thm)],[324, 323])).
% 70.74/70.97 tff(326,plain,
% 70.74/70.97 (k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2)))),
% 70.74/70.97 inference(symmetry,[status(thm)],[325])).
% 70.74/70.98 tff(327,plain,
% 70.74/70.98 (^[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)))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(328,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[327])).
% 70.74/70.98 tff(329,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(rewrite,[status(thm)],[])).
% 70.74/70.98 tff(330,plain,
% 70.74/70.98 (^[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)))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(331,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[330])).
% 70.74/70.98 tff(332,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 70.74/70.98 tff(333,plain,
% 70.74/70.98 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[332, 331])).
% 70.74/70.98 tff(334,plain,
% 70.74/70.98 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[333, 329])).
% 70.74/70.98 tff(335,plain,(
% 70.74/70.98 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 70.74/70.98 inference(skolemize,[status(sab)],[334])).
% 70.74/70.98 tff(336,plain,
% 70.74/70.98 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[335, 328])).
% 70.74/70.98 tff(337,plain,
% 70.74/70.98 (((~![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))))),
% 70.74/70.98 inference(rewrite,[status(thm)],[])).
% 70.74/70.98 tff(338,plain,
% 70.74/70.98 ((~![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))))),
% 70.74/70.98 inference(quant_inst,[status(thm)],[])).
% 70.74/70.98 tff(339,plain,
% 70.74/70.98 ((~![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)))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[338, 337])).
% 70.74/70.98 tff(340,plain,
% 70.74/70.98 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 70.74/70.98 inference(unit_resolution,[status(thm)],[339, 26, 336])).
% 70.74/70.98 tff(341,plain,
% 70.74/70.98 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 70.74/70.98 inference(symmetry,[status(thm)],[340])).
% 70.74/70.98 tff(342,plain,
% 70.74/70.98 (k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))),
% 70.74/70.98 inference(monotonicity,[status(thm)],[341])).
% 70.74/70.98 tff(343,plain,
% 70.74/70.98 (k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k20_filter_2(A!0, B!1, C!2)),
% 70.74/70.98 inference(transitivity,[status(thm)],[342, 326, 174])).
% 70.74/70.98 tff(344,plain,
% 70.74/70.98 (r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) <=> r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))),
% 70.74/70.98 inference(monotonicity,[status(thm)],[160, 343])).
% 70.74/70.98 tff(345,plain,
% 70.74/70.98 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 70.74/70.98 inference(monotonicity,[status(thm)],[341])).
% 70.74/70.98 tff(346,plain,
% 70.74/70.98 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.74/70.98 inference(symmetry,[status(thm)],[345])).
% 70.74/70.98 tff(347,plain,
% 70.74/70.98 (^[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)))))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(348,plain,
% 70.74/70.98 (![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))))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[347])).
% 70.74/70.98 tff(349,plain,
% 70.74/70.98 (^[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))))))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(350,plain,
% 70.74/70.98 (![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))))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[349])).
% 70.74/70.98 tff(351,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(rewrite,[status(thm)],[])).
% 70.74/70.98 tff(352,plain,
% 70.74/70.98 (^[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))))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(353,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[352])).
% 70.74/70.98 tff(354,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 70.74/70.98 tff(355,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[354, 353])).
% 70.74/70.98 tff(356,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[355, 351])).
% 70.74/70.98 tff(357,plain,(
% 70.74/70.98 ![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))))),
% 70.74/70.98 inference(skolemize,[status(sab)],[356])).
% 70.74/70.98 tff(358,plain,
% 70.74/70.98 (![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))))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[357, 350])).
% 70.74/70.98 tff(359,plain,
% 70.74/70.98 (![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))))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[358, 348])).
% 70.74/70.98 tff(360,plain,
% 70.74/70.98 (((~![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))))))),
% 70.74/70.98 inference(rewrite,[status(thm)],[])).
% 70.74/70.98 tff(361,plain,
% 70.74/70.98 ((~![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))))))),
% 70.74/70.98 inference(quant_inst,[status(thm)],[])).
% 70.74/70.98 tff(362,plain,
% 70.74/70.98 ((~![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)))))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[361, 360])).
% 70.74/70.98 tff(363,plain,
% 70.74/70.98 (~(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))))),
% 70.74/70.98 inference(unit_resolution,[status(thm)],[362, 28, 27, 26, 359])).
% 70.74/70.98 tff(364,plain,
% 70.74/70.98 ((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))),
% 70.74/70.98 inference(tautology,[status(thm)],[])).
% 70.74/70.98 tff(365,plain,
% 70.74/70.98 (v10_lattices(k1_lattice2(A!0))),
% 70.74/70.98 inference(unit_resolution,[status(thm)],[364, 363])).
% 70.74/70.98 tff(366,plain,
% 70.74/70.98 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[365, 346])).
% 70.74/70.98 tff(367,plain,
% 70.74/70.98 (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))),
% 70.74/70.98 inference(monotonicity,[status(thm)],[341])).
% 70.74/70.98 tff(368,plain,
% 70.74/70.98 (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)))),
% 70.74/70.98 inference(symmetry,[status(thm)],[367])).
% 70.74/70.98 tff(369,plain,
% 70.74/70.98 ((~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))))),
% 70.74/70.98 inference(monotonicity,[status(thm)],[368])).
% 70.74/70.98 tff(370,plain,
% 70.74/70.98 ((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)))),
% 70.74/70.98 inference(tautology,[status(thm)],[])).
% 70.74/70.98 tff(371,plain,
% 70.74/70.98 (~v3_struct_0(k1_lattice2(A!0))),
% 70.74/70.98 inference(unit_resolution,[status(thm)],[370, 363])).
% 70.74/70.98 tff(372,plain,
% 70.74/70.98 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.74/70.98 inference(modus_ponens,[status(thm)],[371, 369])).
% 70.74/70.98 tff(373,plain,
% 70.74/70.98 (l3_lattices(k1_lattice2(A!0)) <=> l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.74/70.98 inference(monotonicity,[status(thm)],[340])).
% 70.74/70.98 tff(374,plain,
% 70.74/70.98 (^[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)))))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(375,plain,
% 70.74/70.98 (![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))))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[374])).
% 70.74/70.98 tff(376,plain,
% 70.74/70.98 (^[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)))))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(377,plain,
% 70.74/70.98 (![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))))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[376])).
% 70.74/70.98 tff(378,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(rewrite,[status(thm)],[])).
% 70.74/70.98 tff(379,plain,
% 70.74/70.98 (^[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)))))),
% 70.74/70.98 inference(bind,[status(th)],[])).
% 70.74/70.98 tff(380,plain,
% 70.74/70.98 (![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))))),
% 70.74/70.98 inference(quant_intro,[status(thm)],[379])).
% 70.74/70.98 tff(381,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice2')).
% 70.82/70.98 tff(382,plain,
% 70.82/70.98 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[381, 380])).
% 70.82/70.98 tff(383,plain,
% 70.82/70.98 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[382, 378])).
% 70.82/70.98 tff(384,plain,(
% 70.82/70.98 ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 70.82/70.98 inference(skolemize,[status(sab)],[383])).
% 70.82/70.98 tff(385,plain,
% 70.82/70.98 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[384, 377])).
% 70.82/70.98 tff(386,plain,
% 70.82/70.98 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[385, 375])).
% 70.82/70.98 tff(387,plain,
% 70.82/70.98 (((~![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))))))),
% 70.82/70.98 inference(rewrite,[status(thm)],[])).
% 70.82/70.98 tff(388,plain,
% 70.82/70.98 ((~![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))))))),
% 70.82/70.98 inference(quant_inst,[status(thm)],[])).
% 70.82/70.98 tff(389,plain,
% 70.82/70.98 ((~![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)))))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[388, 387])).
% 70.82/70.98 tff(390,plain,
% 70.82/70.98 (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))),
% 70.82/70.98 inference(unit_resolution,[status(thm)],[389, 26, 386])).
% 70.82/70.98 tff(391,plain,
% 70.82/70.98 (((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))) | l3_lattices(k1_lattice2(A!0))),
% 70.82/70.98 inference(tautology,[status(thm)],[])).
% 70.82/70.98 tff(392,plain,
% 70.82/70.98 (l3_lattices(k1_lattice2(A!0))),
% 70.82/70.98 inference(unit_resolution,[status(thm)],[391, 390])).
% 70.82/70.98 tff(393,plain,
% 70.82/70.98 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[392, 373])).
% 70.82/70.98 tff(394,plain,
% 70.82/70.98 (^[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))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(395,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[394])).
% 70.82/70.98 tff(396,plain,
% 70.82/70.98 (^[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))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(397,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[396])).
% 70.82/70.98 tff(398,plain,
% 70.82/70.98 (^[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))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(399,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[398])).
% 70.82/70.98 tff(400,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(transitivity,[status(thm)],[399, 397])).
% 70.82/70.98 tff(401,plain,
% 70.82/70.98 (^[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)))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(402,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[401])).
% 70.82/70.98 tff(403,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(rewrite,[status(thm)],[])).
% 70.82/70.98 tff(404,plain,
% 70.82/70.98 (^[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)))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(405,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[404])).
% 70.82/70.98 tff(406,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 70.82/70.98 tff(407,plain,
% 70.82/70.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[406, 405])).
% 70.82/70.98 tff(408,plain,
% 70.82/70.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[407, 403])).
% 70.82/70.98 tff(409,plain,(
% 70.82/70.98 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 70.82/70.98 inference(skolemize,[status(sab)],[408])).
% 70.82/70.98 tff(410,plain,
% 70.82/70.98 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[409, 402])).
% 70.82/70.98 tff(411,plain,
% 70.82/70.98 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[410, 400])).
% 70.82/70.98 tff(412,plain,
% 70.82/70.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[411, 395])).
% 70.82/70.98 tff(413,plain,
% 70.82/70.98 (((~![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)))))),
% 70.82/70.98 inference(rewrite,[status(thm)],[])).
% 70.82/70.98 tff(414,plain,
% 70.82/70.98 ((~![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)))))),
% 70.82/70.98 inference(quant_inst,[status(thm)],[])).
% 70.82/70.98 tff(415,plain,
% 70.82/70.98 ((~![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))))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[414, 413])).
% 70.82/70.98 tff(416,plain,
% 70.82/70.98 (![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))))),
% 70.82/70.98 inference(unit_resolution,[status(thm)],[415, 412, 393, 372, 366])).
% 70.82/70.98 tff(417,plain,
% 70.82/70.98 ((~![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))))),
% 70.82/70.98 inference(quant_inst,[status(thm)],[])).
% 70.82/70.98 tff(418,plain,
% 70.82/70.98 (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)))),
% 70.82/70.98 inference(unit_resolution,[status(thm)],[417, 416])).
% 70.82/70.98 tff(419,plain,
% 70.82/70.98 (^[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))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(420,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[419])).
% 70.82/70.98 tff(421,plain,
% 70.82/70.98 (^[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)))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(422,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[421])).
% 70.82/70.98 tff(423,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(rewrite,[status(thm)],[])).
% 70.82/70.98 tff(424,plain,
% 70.82/70.98 (^[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)))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(425,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[424])).
% 70.82/70.98 tff(426,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 70.82/70.98 tff(427,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[426, 425])).
% 70.82/70.98 tff(428,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[427, 423])).
% 70.82/70.98 tff(429,plain,(
% 70.82/70.98 ![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)))),
% 70.82/70.98 inference(skolemize,[status(sab)],[428])).
% 70.82/70.98 tff(430,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[429, 422])).
% 70.82/70.98 tff(431,plain,
% 70.82/70.98 (![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)))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[430, 420])).
% 70.82/70.98 tff(432,plain,
% 70.82/70.98 (((~![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)) | (~v10_lattices(A!0)) | (~l3_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)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 70.82/70.98 inference(rewrite,[status(thm)],[])).
% 70.82/70.98 tff(433,plain,
% 70.82/70.98 ((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)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 70.82/70.98 inference(rewrite,[status(thm)],[])).
% 70.82/70.98 tff(434,plain,
% 70.82/70.98 (((~![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)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))))),
% 70.82/70.98 inference(monotonicity,[status(thm)],[433])).
% 70.82/70.98 tff(435,plain,
% 70.82/70.98 (((~![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)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 70.82/70.98 inference(transitivity,[status(thm)],[434, 432])).
% 70.82/70.98 tff(436,plain,
% 70.82/70.98 ((~![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)))),
% 70.82/70.98 inference(quant_inst,[status(thm)],[])).
% 70.82/70.98 tff(437,plain,
% 70.82/70.98 ((~![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)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))),
% 70.82/70.98 inference(modus_ponens,[status(thm)],[436, 435])).
% 70.82/70.98 tff(438,plain,
% 70.82/70.98 (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)),
% 70.82/70.98 inference(unit_resolution,[status(thm)],[437, 28, 27, 26, 145, 431])).
% 70.82/70.98 tff(439,plain,
% 70.82/70.98 (k7_filter_2(A!0, B!1) = k15_filter_2(A!0, B!1)),
% 70.82/70.98 inference(symmetry,[status(thm)],[438])).
% 70.82/70.98 tff(440,plain,
% 70.82/70.98 (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))),
% 70.82/70.98 inference(monotonicity,[status(thm)],[439, 341])).
% 70.82/70.98 tff(441,plain,
% 70.82/70.98 (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)))),
% 70.82/70.98 inference(symmetry,[status(thm)],[440])).
% 70.82/70.98 tff(442,plain,
% 70.82/70.98 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 70.82/70.98 inference(bind,[status(th)],[])).
% 70.82/70.98 tff(443,plain,
% 70.82/70.98 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.82/70.98 inference(quant_intro,[status(thm)],[442])).
% 70.82/70.98 tff(444,plain,
% 70.82/70.98 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 70.82/70.99 inference(bind,[status(th)],[])).
% 70.82/70.99 tff(445,plain,
% 70.82/70.99 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.82/70.99 inference(quant_intro,[status(thm)],[444])).
% 70.82/70.99 tff(446,plain,
% 70.82/70.99 (![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)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(447,plain,
% 70.82/70.99 (^[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)))))),
% 70.82/70.99 inference(bind,[status(th)],[])).
% 70.82/70.99 tff(448,plain,
% 70.82/70.99 (![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)))),
% 70.82/70.99 inference(quant_intro,[status(thm)],[447])).
% 70.82/70.99 tff(449,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k15_filter_2')).
% 70.82/70.99 tff(450,plain,
% 70.82/70.99 (![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)))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[449, 448])).
% 70.82/70.99 tff(451,plain,
% 70.82/70.99 (![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)))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[450, 446])).
% 70.82/70.99 tff(452,plain,(
% 70.82/70.99 ![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)))),
% 70.82/70.99 inference(skolemize,[status(sab)],[451])).
% 70.82/70.99 tff(453,plain,
% 70.82/70.99 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[452, 445])).
% 70.82/70.99 tff(454,plain,
% 70.82/70.99 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[453, 443])).
% 70.82/70.99 tff(455,plain,
% 70.82/70.99 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(456,plain,
% 70.82/70.99 ((v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(457,plain,
% 70.82/70.99 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 70.82/70.99 inference(monotonicity,[status(thm)],[456])).
% 70.82/70.99 tff(458,plain,
% 70.82/70.99 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 70.82/70.99 inference(transitivity,[status(thm)],[457, 455])).
% 70.82/70.99 tff(459,plain,
% 70.82/70.99 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.82/70.99 inference(quant_inst,[status(thm)],[])).
% 70.82/70.99 tff(460,plain,
% 70.82/70.99 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[459, 458])).
% 70.82/70.99 tff(461,plain,
% 70.82/70.99 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[460, 28, 27, 26, 145, 454])).
% 70.82/70.99 tff(462,plain,
% 70.82/70.99 (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)))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[461, 441])).
% 70.82/70.99 tff(463,plain,
% 70.82/70.99 ((~(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)))),
% 70.82/70.99 inference(tautology,[status(thm)],[])).
% 70.82/70.99 tff(464,plain,
% 70.82/70.99 (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)))),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[463, 462, 418])).
% 70.82/70.99 tff(465,plain,
% 70.82/70.99 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))))),
% 70.82/70.99 inference(bind,[status(th)],[])).
% 70.82/70.99 tff(466,plain,
% 70.82/70.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(quant_intro,[status(thm)],[465])).
% 70.82/70.99 tff(467,plain,
% 70.82/70.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))))),
% 70.82/70.99 inference(bind,[status(th)],[])).
% 70.82/70.99 tff(468,plain,
% 70.82/70.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(quant_intro,[status(thm)],[467])).
% 70.82/70.99 tff(469,plain,
% 70.82/70.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(transitivity,[status(thm)],[468, 466])).
% 70.82/70.99 tff(470,plain,
% 70.82/70.99 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))))),
% 70.82/70.99 inference(bind,[status(th)],[])).
% 70.82/70.99 tff(471,plain,
% 70.82/70.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(quant_intro,[status(thm)],[470])).
% 70.82/70.99 tff(472,plain,
% 70.82/70.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(473,plain,
% 70.82/70.99 (^[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(quant_intro(proof_bind(^[C: $i] : rewrite((m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))) <=> ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))), (![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))) <=> ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))), ((m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))) <=> (m1_filter_0(B, A) => ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))), rewrite((m1_filter_0(B, A) => ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))), ((m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))))), (![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(bind,[status(th)],[])).
% 70.82/70.99 tff(474,plain,
% 70.82/70.99 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))),
% 70.82/70.99 inference(quant_intro,[status(thm)],[473])).
% 70.82/70.99 tff(475,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t49_filter_0')).
% 70.82/70.99 tff(476,plain,
% 70.82/70.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[475, 474])).
% 70.82/70.99 tff(477,plain,
% 70.82/70.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[476, 472])).
% 70.82/70.99 tff(478,plain,(
% 70.82/70.99 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (r1_tarski(B, k5_filter_0(A, B, C)) & r1_tarski(C, k5_filter_0(A, B, C))))))),
% 70.82/70.99 inference(skolemize,[status(sab)],[477])).
% 70.82/70.99 tff(479,plain,
% 70.82/70.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[478, 471])).
% 70.82/70.99 tff(480,plain,
% 70.82/70.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[479, 469])).
% 70.82/70.99 tff(481,plain,
% 70.82/70.99 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))))))))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(482,plain,
% 70.82/70.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))))))))),
% 70.82/70.99 inference(quant_inst,[status(thm)],[])).
% 70.82/70.99 tff(483,plain,
% 70.82/70.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (~((~r1_tarski(B, k5_filter_0(A, B, C))) | (~r1_tarski(C, k5_filter_0(A, B, C))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[482, 481])).
% 70.82/70.99 tff(484,plain,
% 70.82/70.99 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))))),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[483, 480, 393, 372, 366])).
% 70.82/70.99 tff(485,plain,
% 70.82/70.99 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))))) | ((~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)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))))) | (~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)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C)))))))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(486,plain,
% 70.82/70.99 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))))) | ((~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)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C)))))))),
% 70.82/70.99 inference(quant_inst,[status(thm)],[])).
% 70.82/70.99 tff(487,plain,
% 70.82/70.99 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(B, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))))) | (~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)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[486, 485])).
% 70.82/70.99 tff(488,plain,
% 70.82/70.99 ((~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)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[487, 484])).
% 70.82/70.99 tff(489,plain,
% 70.82/70.99 (![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[488, 464])).
% 70.82/70.99 tff(490,plain,
% 70.82/70.99 ((~![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, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 70.82/70.99 inference(quant_inst,[status(thm)],[])).
% 70.82/70.99 tff(491,plain,
% 70.82/70.99 (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[490, 416])).
% 70.82/70.99 tff(492,plain,
% 70.82/70.99 (((~![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(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))) <=> ((~![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(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(493,plain,
% 70.82/70.99 ((v3_struct_0(A!0) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(494,plain,
% 70.82/70.99 (((~![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, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, 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(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2))))),
% 70.82/70.99 inference(monotonicity,[status(thm)],[493])).
% 70.82/70.99 tff(495,plain,
% 70.82/70.99 (((~![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, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, 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(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 70.82/70.99 inference(transitivity,[status(thm)],[494, 492])).
% 70.82/70.99 tff(496,plain,
% 70.82/70.99 ((~![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, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.82/70.99 inference(quant_inst,[status(thm)],[])).
% 70.82/70.99 tff(497,plain,
% 70.82/70.99 ((~![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(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2))),
% 70.82/70.99 inference(modus_ponens,[status(thm)],[496, 495])).
% 70.82/70.99 tff(498,plain,
% 70.82/70.99 (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)),
% 70.82/70.99 inference(unit_resolution,[status(thm)],[497, 28, 27, 26, 34, 431])).
% 70.82/70.99 tff(499,plain,
% 70.82/70.99 (k7_filter_2(A!0, C!2) = k15_filter_2(A!0, C!2)),
% 70.82/70.99 inference(symmetry,[status(thm)],[498])).
% 70.82/70.99 tff(500,plain,
% 70.82/70.99 (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 70.82/70.99 inference(monotonicity,[status(thm)],[499, 341])).
% 70.82/70.99 tff(501,plain,
% 70.82/70.99 (m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) <=> m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.82/70.99 inference(symmetry,[status(thm)],[500])).
% 70.82/70.99 tff(502,plain,
% 70.82/70.99 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(503,plain,
% 70.82/70.99 ((v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 70.82/70.99 inference(rewrite,[status(thm)],[])).
% 70.82/70.99 tff(504,plain,
% 70.82/70.99 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))))),
% 70.82/70.99 inference(monotonicity,[status(thm)],[503])).
% 70.82/70.99 tff(505,plain,
% 70.82/70.99 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 70.82/70.99 inference(transitivity,[status(thm)],[504, 502])).
% 70.82/70.99 tff(506,plain,
% 70.82/70.99 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 70.82/70.99 inference(quant_inst,[status(thm)],[])).
% 70.82/70.99 tff(507,plain,
% 70.82/70.99 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 70.82/71.00 inference(modus_ponens,[status(thm)],[506, 505])).
% 70.82/71.00 tff(508,plain,
% 70.82/71.00 (m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 70.82/71.00 inference(unit_resolution,[status(thm)],[507, 28, 27, 26, 34, 454])).
% 70.82/71.00 tff(509,plain,
% 70.82/71.00 (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.82/71.00 inference(modus_ponens,[status(thm)],[508, 501])).
% 70.82/71.00 tff(510,plain,
% 70.82/71.00 ((~(m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.82/71.00 inference(tautology,[status(thm)],[])).
% 70.82/71.00 tff(511,plain,
% 70.82/71.00 (m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 70.82/71.00 inference(unit_resolution,[status(thm)],[510, 509, 491])).
% 70.82/71.00 tff(512,plain,
% 70.82/71.00 (((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))) | ((~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))) <=> ((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))) | (~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))),
% 70.82/71.00 inference(rewrite,[status(thm)],[])).
% 70.82/71.00 tff(513,plain,
% 70.82/71.00 ((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))) | ((~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))),
% 70.82/71.00 inference(quant_inst,[status(thm)],[])).
% 70.82/71.00 tff(514,plain,
% 70.82/71.00 ((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))) | (~r1_tarski(C, k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))))) | (~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))))),
% 70.82/71.00 inference(modus_ponens,[status(thm)],[513, 512])).
% 70.82/71.00 tff(515,plain,
% 70.82/71.00 (~((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 70.82/71.00 inference(unit_resolution,[status(thm)],[514, 511, 489])).
% 70.82/71.00 tff(516,plain,
% 70.82/71.00 (((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))) | r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 70.82/71.00 inference(tautology,[status(thm)],[])).
% 70.82/71.00 tff(517,plain,
% 70.82/71.00 (r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 70.82/71.00 inference(unit_resolution,[status(thm)],[516, 515])).
% 70.82/71.00 tff(518,plain,
% 70.82/71.00 (r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))),
% 70.82/71.00 inference(modus_ponens,[status(thm)],[517, 344])).
% 70.82/71.00 tff(519,plain,
% 70.82/71.00 (r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) <=> r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))),
% 70.82/71.00 inference(monotonicity,[status(thm)],[95, 343])).
% 70.82/71.00 tff(520,plain,
% 70.82/71.00 (((~r1_tarski(k7_filter_2(A!0, B!1), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) | (~r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))) | r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 70.82/71.00 inference(tautology,[status(thm)],[])).
% 70.82/71.00 tff(521,plain,
% 70.82/71.00 (r1_tarski(k7_filter_2(A!0, C!2), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 70.82/71.00 inference(unit_resolution,[status(thm)],[520, 515])).
% 70.82/71.00 tff(522,plain,
% 70.82/71.00 (r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))),
% 70.82/71.00 inference(modus_ponens,[status(thm)],[521, 519])).
% 70.82/71.00 tff(523,plain,
% 70.82/71.00 ((~(~((~r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))) | (~r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))))) <=> ((~r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))) | (~r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))))),
% 70.82/71.00 inference(rewrite,[status(thm)],[])).
% 70.82/71.00 tff(524,plain,
% 70.82/71.00 ((r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))) <=> (~((~r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))) | (~r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))))),
% 70.82/71.00 inference(rewrite,[status(thm)],[])).
% 70.82/71.00 tff(525,plain,
% 70.82/71.00 ((~(r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))) <=> (~(~((~r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))) | (~r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))))))),
% 70.82/71.00 inference(monotonicity,[status(thm)],[524])).
% 70.82/71.00 tff(526,plain,
% 70.82/71.00 ((~(r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))) <=> ((~r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))) | (~r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))))),
% 71.06/71.27 inference(transitivity,[status(thm)],[525, 523])).
% 71.06/71.27 tff(527,plain,
% 71.06/71.27 (~(r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2)) & r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))),
% 71.06/71.27 inference(or_elim,[status(thm)],[33])).
% 71.06/71.27 tff(528,plain,
% 71.06/71.27 ((~r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))) | (~r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2)))),
% 71.06/71.27 inference(modus_ponens,[status(thm)],[527, 526])).
% 71.06/71.27 tff(529,plain,
% 71.06/71.27 ($false),
% 71.06/71.27 inference(unit_resolution,[status(thm)],[528, 522, 518])).
% 71.06/71.27 % SZS output end Proof
% 71.06/71.27 % E exiting
%------------------------------------------------------------------------------