TSTP Solution File: LAT317+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT317+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:01 EDT 2022
% Result : Theorem 102.45s 66.12s
% Output : Proof 102.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT317+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 14:26:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 102.45/66.12 % SZS status Theorem
% 102.45/66.12 % SZS output start Proof
% 102.45/66.12 tff(r1_tarski_type, type, (
% 102.45/66.12 r1_tarski: ( $i * $i ) > $o)).
% 102.45/66.12 tff(k20_filter_2_type, type, (
% 102.45/66.12 k20_filter_2: ( $i * $i * $i ) > $i)).
% 102.45/66.12 tff(tptp_fun_C_2_type, type, (
% 102.45/66.12 tptp_fun_C_2: $i)).
% 102.45/66.12 tff(tptp_fun_B_1_type, type, (
% 102.45/66.12 tptp_fun_B_1: $i)).
% 102.45/66.12 tff(tptp_fun_A_0_type, type, (
% 102.45/66.12 tptp_fun_A_0: $i)).
% 102.45/66.12 tff(k5_filter_0_type, type, (
% 102.45/66.12 k5_filter_0: ( $i * $i * $i ) > $i)).
% 102.45/66.12 tff(k7_filter_2_type, type, (
% 102.45/66.12 k7_filter_2: ( $i * $i ) > $i)).
% 102.45/66.12 tff(g3_lattices_type, type, (
% 102.45/66.12 g3_lattices: ( $i * $i * $i ) > $i)).
% 102.45/66.12 tff(u2_lattices_type, type, (
% 102.45/66.12 u2_lattices: $i > $i)).
% 102.45/66.12 tff(u1_lattices_type, type, (
% 102.45/66.12 u1_lattices: $i > $i)).
% 102.45/66.12 tff(u1_struct_0_type, type, (
% 102.45/66.12 u1_struct_0: $i > $i)).
% 102.45/66.12 tff(k8_filter_2_type, type, (
% 102.45/66.12 k8_filter_2: ( $i * $i ) > $i)).
% 102.45/66.12 tff(m1_subset_1_type, type, (
% 102.45/66.12 m1_subset_1: ( $i * $i ) > $o)).
% 102.45/66.12 tff(k1_zfmisc_1_type, type, (
% 102.45/66.12 k1_zfmisc_1: $i > $i)).
% 102.45/66.12 tff(m2_lattice4_type, type, (
% 102.45/66.12 m2_lattice4: ( $i * $i ) > $o)).
% 102.45/66.12 tff(v1_xboole_0_type, type, (
% 102.45/66.12 v1_xboole_0: $i > $o)).
% 102.45/66.12 tff(m2_filter_2_type, type, (
% 102.45/66.12 m2_filter_2: ( $i * $i ) > $o)).
% 102.45/66.12 tff(v10_lattices_type, type, (
% 102.45/66.12 v10_lattices: $i > $o)).
% 102.45/66.12 tff(l3_lattices_type, type, (
% 102.45/66.12 l3_lattices: $i > $o)).
% 102.45/66.12 tff(v3_struct_0_type, type, (
% 102.45/66.12 v3_struct_0: $i > $o)).
% 102.45/66.12 tff(k1_lattice2_type, type, (
% 102.45/66.12 k1_lattice2: $i > $i)).
% 102.45/66.12 tff(tptp_fun_B_7_type, type, (
% 102.45/66.12 tptp_fun_B_7: $i > $i)).
% 102.45/66.12 tff(tptp_fun_B_19_type, type, (
% 102.45/66.12 tptp_fun_B_19: $i > $i)).
% 102.45/66.12 tff(m1_filter_0_type, type, (
% 102.45/66.12 m1_filter_0: ( $i * $i ) > $o)).
% 102.45/66.12 tff(m1_filter_2_type, type, (
% 102.45/66.12 m1_filter_2: ( $i * $i ) > $o)).
% 102.45/66.12 tff(v9_lattices_type, type, (
% 102.45/66.12 v9_lattices: $i > $o)).
% 102.45/66.12 tff(v8_lattices_type, type, (
% 102.45/66.12 v8_lattices: $i > $o)).
% 102.45/66.12 tff(v7_lattices_type, type, (
% 102.45/66.12 v7_lattices: $i > $o)).
% 102.45/66.12 tff(v6_lattices_type, type, (
% 102.45/66.12 v6_lattices: $i > $o)).
% 102.45/66.12 tff(v5_lattices_type, type, (
% 102.45/66.12 v5_lattices: $i > $o)).
% 102.45/66.12 tff(v4_lattices_type, type, (
% 102.45/66.12 v4_lattices: $i > $o)).
% 102.45/66.12 tff(v3_lattices_type, type, (
% 102.45/66.12 v3_lattices: $i > $o)).
% 102.45/66.12 tff(k15_filter_2_type, type, (
% 102.45/66.12 k15_filter_2: ( $i * $i ) > $i)).
% 102.45/66.12 tff(1,plain,
% 102.45/66.12 (^[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)))))))),
% 102.45/66.12 inference(bind,[status(th)],[])).
% 102.45/66.12 tff(2,plain,
% 102.45/66.12 (![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))))))),
% 102.45/66.12 inference(quant_intro,[status(thm)],[1])).
% 102.45/66.12 tff(3,plain,
% 102.45/66.12 (^[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)))))))),
% 102.45/66.12 inference(bind,[status(th)],[])).
% 102.45/66.12 tff(4,plain,
% 102.45/66.12 (![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))))))),
% 102.45/66.12 inference(quant_intro,[status(thm)],[3])).
% 102.45/66.12 tff(5,plain,
% 102.45/66.12 (![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))))))),
% 102.45/66.12 inference(transitivity,[status(thm)],[4, 2])).
% 102.45/66.12 tff(6,plain,
% 102.45/66.12 (^[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))))))))),
% 102.45/66.12 inference(bind,[status(th)],[])).
% 102.45/66.12 tff(7,plain,
% 102.45/66.12 (![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))))))),
% 102.45/66.12 inference(quant_intro,[status(thm)],[6])).
% 102.45/66.12 tff(8,plain,
% 102.45/66.12 (![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))))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(9,plain,
% 102.45/66.12 (^[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))))))),
% 102.45/66.12 inference(bind,[status(th)],[])).
% 102.45/66.12 tff(10,plain,
% 102.45/66.12 (![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))))),
% 102.45/66.12 inference(quant_intro,[status(thm)],[9])).
% 102.45/66.12 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/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 102.45/66.12 tff(12,plain,
% 102.45/66.12 (![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))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[11, 10])).
% 102.45/66.12 tff(13,plain,
% 102.45/66.12 (![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))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[12, 8])).
% 102.45/66.12 tff(14,plain,(
% 102.45/66.12 ![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))))),
% 102.45/66.12 inference(skolemize,[status(sab)],[13])).
% 102.45/66.12 tff(15,plain,
% 102.45/66.12 (![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[14, 7])).
% 102.45/66.12 tff(16,plain,
% 102.45/66.12 (![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[15, 5])).
% 102.45/66.12 tff(17,plain,
% 102.45/66.12 ((((~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))))))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(18,plain,
% 102.45/66.12 (((~(~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)))))) <=> (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))))))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(19,plain,
% 102.45/66.12 ((~(~((~v3_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))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(20,plain,
% 102.45/66.12 (((~(~((~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)))))))),
% 102.45/66.12 inference(monotonicity,[status(thm)],[19, 18])).
% 102.45/66.12 tff(21,plain,
% 102.45/66.12 (((~(~((~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))))))),
% 102.45/66.12 inference(transitivity,[status(thm)],[20, 17])).
% 102.45/66.12 tff(22,plain,
% 102.45/66.12 ((~![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)))))))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(23,plain,
% 102.45/66.12 ((~![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)))))))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(24,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/sandbox/benchmark/theBenchmark.p','t51_filter_2')).
% 102.45/66.12 tff(25,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[24, 23])).
% 102.45/66.12 tff(26,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[25, 22])).
% 102.45/66.12 tff(27,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[26, 22])).
% 102.45/66.12 tff(28,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[27, 22])).
% 102.45/66.12 tff(29,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[28, 22])).
% 102.45/66.12 tff(30,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[29, 22])).
% 102.45/66.12 tff(31,plain,
% 102.45/66.12 (~![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))))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[30, 22])).
% 102.45/66.12 tff(32,plain,
% 102.45/66.12 ((~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)))))),
% 102.45/66.12 inference(modus_ponens,[status(thm)],[31, 21])).
% 102.45/66.12 tff(33,plain,
% 102.45/66.12 (l3_lattices(A!0)),
% 102.45/66.12 inference(and_elim,[status(thm)],[32])).
% 102.45/66.12 tff(34,plain,
% 102.45/66.12 (v10_lattices(A!0)),
% 102.45/66.12 inference(and_elim,[status(thm)],[32])).
% 102.45/66.12 tff(35,plain,
% 102.45/66.12 (~v3_struct_0(A!0)),
% 102.45/66.12 inference(and_elim,[status(thm)],[32])).
% 102.45/66.12 tff(36,plain,
% 102.45/66.12 (((~![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))))))),
% 102.45/66.12 inference(rewrite,[status(thm)],[])).
% 102.45/66.12 tff(37,plain,
% 102.45/66.12 ((~![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))))))),
% 102.49/66.12 inference(quant_inst,[status(thm)],[])).
% 102.49/66.12 tff(38,plain,
% 102.49/66.12 ((~![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)))))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[37, 36])).
% 102.49/66.12 tff(39,plain,
% 102.49/66.12 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 16])).
% 102.49/66.12 tff(40,plain,
% 102.49/66.12 (~((~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))))),
% 102.49/66.12 inference(and_elim,[status(thm)],[32])).
% 102.49/66.12 tff(41,plain,
% 102.49/66.12 (m2_filter_2(C!2, A!0)),
% 102.49/66.12 inference(or_elim,[status(thm)],[40])).
% 102.49/66.12 tff(42,plain,
% 102.49/66.12 (((~![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)))))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(43,plain,
% 102.49/66.12 ((~![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)))))),
% 102.49/66.12 inference(quant_inst,[status(thm)],[])).
% 102.49/66.12 tff(44,plain,
% 102.49/66.12 ((~![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))))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[43, 42])).
% 102.49/66.12 tff(45,plain,
% 102.49/66.12 (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[44, 41, 39])).
% 102.49/66.12 tff(46,plain,
% 102.49/66.12 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | m2_lattice4(C!2, A!0)),
% 102.49/66.12 inference(tautology,[status(thm)],[])).
% 102.49/66.12 tff(47,plain,
% 102.49/66.12 (m2_lattice4(C!2, A!0)),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[46, 45])).
% 102.49/66.12 tff(48,plain,
% 102.49/66.12 (^[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))))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(49,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[48])).
% 102.49/66.12 tff(50,plain,
% 102.49/66.12 (^[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))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(51,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[50])).
% 102.49/66.12 tff(52,plain,
% 102.49/66.12 (^[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))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(53,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[52])).
% 102.49/66.12 tff(54,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(transitivity,[status(thm)],[53, 51])).
% 102.49/66.12 tff(55,plain,
% 102.49/66.12 (^[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)))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(56,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[55])).
% 102.49/66.12 tff(57,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(58,plain,
% 102.49/66.12 (^[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)))))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(59,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[58])).
% 102.49/66.12 tff(60,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 102.49/66.12 tff(61,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[60, 59])).
% 102.49/66.12 tff(62,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[61, 57])).
% 102.49/66.12 tff(63,plain,(
% 102.49/66.12 ![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)))))),
% 102.49/66.12 inference(skolemize,[status(sab)],[62])).
% 102.49/66.12 tff(64,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[63, 56])).
% 102.49/66.12 tff(65,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[64, 54])).
% 102.49/66.12 tff(66,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[65, 49])).
% 102.49/66.12 tff(67,plain,
% 102.49/66.12 (((~![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)))))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(68,plain,
% 102.49/66.12 ((~![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)))))),
% 102.49/66.12 inference(quant_inst,[status(thm)],[])).
% 102.49/66.12 tff(69,plain,
% 102.49/66.12 ((~![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))))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[68, 67])).
% 102.49/66.12 tff(70,plain,
% 102.49/66.12 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[69, 35, 34, 33, 66])).
% 102.49/66.12 tff(71,plain,
% 102.49/66.12 (((~![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))))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(72,plain,
% 102.49/66.12 ((~![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))))),
% 102.49/66.12 inference(quant_inst,[status(thm)],[])).
% 102.49/66.12 tff(73,plain,
% 102.49/66.12 ((~![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[72, 71])).
% 102.49/66.12 tff(74,plain,
% 102.49/66.12 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[73, 70, 47])).
% 102.49/66.12 tff(75,plain,
% 102.49/66.12 (^[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))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(76,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[75])).
% 102.49/66.12 tff(77,plain,
% 102.49/66.12 (^[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))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(78,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[77])).
% 102.49/66.12 tff(79,plain,
% 102.49/66.12 (^[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))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(80,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[79])).
% 102.49/66.12 tff(81,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(transitivity,[status(thm)],[80, 78])).
% 102.49/66.12 tff(82,plain,
% 102.49/66.12 (^[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)))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(83,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[82])).
% 102.49/66.12 tff(84,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(85,plain,
% 102.49/66.12 (^[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)))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(86,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[85])).
% 102.49/66.12 tff(87,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_filter_2')).
% 102.49/66.12 tff(88,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[87, 86])).
% 102.49/66.12 tff(89,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[88, 84])).
% 102.49/66.12 tff(90,plain,(
% 102.49/66.12 ![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)))),
% 102.49/66.12 inference(skolemize,[status(sab)],[89])).
% 102.49/66.12 tff(91,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[90, 83])).
% 102.49/66.12 tff(92,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[91, 81])).
% 102.49/66.12 tff(93,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[92, 76])).
% 102.49/66.12 tff(94,plain,
% 102.49/66.12 (((~![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)))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(95,plain,
% 102.49/66.12 ((~![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)))),
% 102.49/66.12 inference(quant_inst,[status(thm)],[])).
% 102.49/66.12 tff(96,plain,
% 102.49/66.12 ((~![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))),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[95, 94])).
% 102.49/66.12 tff(97,plain,
% 102.49/66.12 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[96, 35, 34, 33, 93])).
% 102.49/66.12 tff(98,plain,
% 102.49/66.12 (((~![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))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(99,plain,
% 102.49/66.12 ((~![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))),
% 102.49/66.12 inference(quant_inst,[status(thm)],[])).
% 102.49/66.12 tff(100,plain,
% 102.49/66.12 ((~![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)),
% 102.49/66.12 inference(modus_ponens,[status(thm)],[99, 98])).
% 102.49/66.12 tff(101,plain,
% 102.49/66.12 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2)),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[100, 97])).
% 102.49/66.12 tff(102,plain,
% 102.49/66.12 (k7_filter_2(A!0, C!2) = C!2),
% 102.49/66.12 inference(unit_resolution,[status(thm)],[101, 74])).
% 102.49/66.12 tff(103,plain,
% 102.49/66.12 (^[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))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(104,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[103])).
% 102.49/66.12 tff(105,plain,
% 102.49/66.12 (^[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)))))),
% 102.49/66.12 inference(bind,[status(th)],[])).
% 102.49/66.12 tff(106,plain,
% 102.49/66.12 (![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)))),
% 102.49/66.12 inference(quant_intro,[status(thm)],[105])).
% 102.49/66.12 tff(107,plain,
% 102.49/66.12 (![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)))))),
% 102.49/66.12 inference(rewrite,[status(thm)],[])).
% 102.49/66.12 tff(108,plain,
% 102.49/66.12 (^[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)))))))),
% 102.49/66.13 inference(bind,[status(th)],[])).
% 102.49/66.13 tff(109,plain,
% 102.49/66.13 (![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)))))),
% 102.49/66.13 inference(quant_intro,[status(thm)],[108])).
% 102.49/66.13 tff(110,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/sandbox/benchmark/theBenchmark.p','dt_k7_filter_2')).
% 102.49/66.13 tff(111,plain,
% 102.49/66.13 (![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)))))),
% 102.49/66.13 inference(modus_ponens,[status(thm)],[110, 109])).
% 102.49/66.13 tff(112,plain,
% 102.49/66.13 (![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)))))),
% 102.49/66.13 inference(modus_ponens,[status(thm)],[111, 107])).
% 102.49/66.13 tff(113,plain,(
% 102.49/66.13 ![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)))))),
% 102.49/66.13 inference(skolemize,[status(sab)],[112])).
% 102.49/66.13 tff(114,plain,
% 102.49/66.13 (![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)))),
% 102.49/66.13 inference(modus_ponens,[status(thm)],[113, 106])).
% 102.49/66.13 tff(115,plain,
% 102.49/66.13 (![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)))),
% 102.49/66.13 inference(modus_ponens,[status(thm)],[114, 104])).
% 102.49/66.13 tff(116,plain,
% 102.49/66.13 (((~![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) | (~l3_lattices(A!0)) | (~v10_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) | (~l3_lattices(A!0)) | (~v10_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)))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(117,plain,
% 102.50/66.13 ((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) | (~l3_lattices(A!0)) | (~v10_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)))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(118,plain,
% 102.50/66.13 (((~![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) | (~l3_lattices(A!0)) | (~v10_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))))))),
% 102.50/66.13 inference(monotonicity,[status(thm)],[117])).
% 102.50/66.13 tff(119,plain,
% 102.50/66.13 (((~![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) | (~l3_lattices(A!0)) | (~v10_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)))))),
% 102.50/66.13 inference(transitivity,[status(thm)],[118, 116])).
% 102.50/66.13 tff(120,plain,
% 102.50/66.13 ((~![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)))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(121,plain,
% 102.50/66.13 ((~![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) | (~l3_lattices(A!0)) | (~v10_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))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[120, 119])).
% 102.50/66.13 tff(122,plain,
% 102.50/66.13 ((~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))))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[121, 35, 34, 33, 115])).
% 102.50/66.13 tff(123,plain,
% 102.50/66.13 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[122, 74])).
% 102.50/66.13 tff(124,plain,
% 102.50/66.13 (^[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))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(125,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[124])).
% 102.50/66.13 tff(126,plain,
% 102.50/66.13 (^[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))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(127,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[126])).
% 102.50/66.13 tff(128,plain,
% 102.50/66.13 (^[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))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(129,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[128])).
% 102.50/66.13 tff(130,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(transitivity,[status(thm)],[129, 127])).
% 102.50/66.13 tff(131,plain,
% 102.50/66.13 (^[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)))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(132,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[131])).
% 102.50/66.13 tff(133,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(134,plain,
% 102.50/66.13 (^[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)))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(135,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[134])).
% 102.50/66.13 tff(136,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/sandbox/benchmark/theBenchmark.p','d7_filter_2')).
% 102.50/66.13 tff(137,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[136, 135])).
% 102.50/66.13 tff(138,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[137, 133])).
% 102.50/66.13 tff(139,plain,(
% 102.50/66.13 ![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)))),
% 102.50/66.13 inference(skolemize,[status(sab)],[138])).
% 102.50/66.13 tff(140,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[139, 132])).
% 102.50/66.13 tff(141,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[140, 130])).
% 102.50/66.13 tff(142,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[141, 125])).
% 102.50/66.13 tff(143,plain,
% 102.50/66.13 (((~![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)))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(144,plain,
% 102.50/66.13 ((~![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)))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(145,plain,
% 102.50/66.13 ((~![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))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[144, 143])).
% 102.50/66.13 tff(146,plain,
% 102.50/66.13 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[145, 35, 34, 33, 142])).
% 102.50/66.13 tff(147,plain,
% 102.50/66.13 (((~![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)))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(148,plain,
% 102.50/66.13 ((~![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)))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(149,plain,
% 102.50/66.13 ((~![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))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[148, 147])).
% 102.50/66.13 tff(150,plain,
% 102.50/66.13 (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[149, 146, 123])).
% 102.50/66.13 tff(151,plain,
% 102.50/66.13 (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = C!2),
% 102.50/66.13 inference(transitivity,[status(thm)],[150, 102])).
% 102.50/66.13 tff(152,plain,
% 102.50/66.13 (m2_filter_2(B!1, A!0)),
% 102.50/66.13 inference(and_elim,[status(thm)],[32])).
% 102.50/66.13 tff(153,plain,
% 102.50/66.13 (((~![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)))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(154,plain,
% 102.50/66.13 ((~![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)))))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(155,plain,
% 102.50/66.13 ((~![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))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[154, 153])).
% 102.50/66.13 tff(156,plain,
% 102.50/66.13 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[155, 152, 39])).
% 102.50/66.13 tff(157,plain,
% 102.50/66.13 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 102.50/66.13 inference(tautology,[status(thm)],[])).
% 102.50/66.13 tff(158,plain,
% 102.50/66.13 (m2_lattice4(B!1, A!0)),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[157, 156])).
% 102.50/66.13 tff(159,plain,
% 102.50/66.13 (((~![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))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(160,plain,
% 102.50/66.13 ((~![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))))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(161,plain,
% 102.50/66.13 ((~![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)))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[160, 159])).
% 102.50/66.13 tff(162,plain,
% 102.50/66.13 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[161, 70, 158])).
% 102.50/66.13 tff(163,plain,
% 102.50/66.13 (((~![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))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(164,plain,
% 102.50/66.13 ((~![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))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(165,plain,
% 102.50/66.13 ((~![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)),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[164, 163])).
% 102.50/66.13 tff(166,plain,
% 102.50/66.13 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[165, 97])).
% 102.50/66.13 tff(167,plain,
% 102.50/66.13 (k7_filter_2(A!0, B!1) = B!1),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[166, 162])).
% 102.50/66.13 tff(168,plain,
% 102.50/66.13 (((~![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) | (~l3_lattices(A!0)) | (~v10_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) | (~l3_lattices(A!0)) | (~v10_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)))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(169,plain,
% 102.50/66.13 ((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) | (~l3_lattices(A!0)) | (~v10_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)))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(170,plain,
% 102.50/66.13 (((~![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) | (~l3_lattices(A!0)) | (~v10_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))))))),
% 102.50/66.13 inference(monotonicity,[status(thm)],[169])).
% 102.50/66.13 tff(171,plain,
% 102.50/66.13 (((~![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) | (~l3_lattices(A!0)) | (~v10_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)))))),
% 102.50/66.13 inference(transitivity,[status(thm)],[170, 168])).
% 102.50/66.13 tff(172,plain,
% 102.50/66.13 ((~![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)))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(173,plain,
% 102.50/66.13 ((~![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) | (~l3_lattices(A!0)) | (~v10_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))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[172, 171])).
% 102.50/66.13 tff(174,plain,
% 102.50/66.13 ((~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))))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[173, 35, 34, 33, 115])).
% 102.50/66.13 tff(175,plain,
% 102.50/66.13 (m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[174, 162])).
% 102.50/66.13 tff(176,plain,
% 102.50/66.13 (((~![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)))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(177,plain,
% 102.50/66.13 ((~![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)))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(178,plain,
% 102.50/66.13 ((~![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))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[177, 176])).
% 102.50/66.13 tff(179,plain,
% 102.50/66.13 (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[178, 146, 175])).
% 102.50/66.13 tff(180,plain,
% 102.50/66.13 (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = B!1),
% 102.50/66.13 inference(transitivity,[status(thm)],[179, 167])).
% 102.50/66.13 tff(181,plain,
% 102.50/66.13 (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)),
% 102.50/66.13 inference(monotonicity,[status(thm)],[180, 151])).
% 102.50/66.13 tff(182,plain,
% 102.50/66.13 (^[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)))))))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(183,plain,
% 102.50/66.13 (![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))))))))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[182])).
% 102.50/66.13 tff(184,plain,
% 102.50/66.13 (^[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)))))))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(185,plain,
% 102.50/66.13 (![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))))))))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[184])).
% 102.50/66.13 tff(186,plain,
% 102.50/66.13 (![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))))))))),
% 102.50/66.13 inference(transitivity,[status(thm)],[185, 183])).
% 102.50/66.13 tff(187,plain,
% 102.50/66.13 (^[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))))))))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(188,plain,
% 102.50/66.13 (![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))))))))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[187])).
% 102.50/66.13 tff(189,plain,
% 102.50/66.13 (![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))))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(190,plain,
% 102.50/66.13 (^[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))))))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(191,plain,
% 102.50/66.13 (![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))))))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[190])).
% 102.50/66.13 tff(192,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/sandbox/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 102.50/66.13 tff(193,plain,
% 102.50/66.13 (![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))))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[192, 191])).
% 102.50/66.13 tff(194,plain,
% 102.50/66.13 (![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))))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[193, 189])).
% 102.50/66.13 tff(195,plain,(
% 102.50/66.13 ![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))))))),
% 102.50/66.13 inference(skolemize,[status(sab)],[194])).
% 102.50/66.13 tff(196,plain,
% 102.50/66.13 (![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))))))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[195, 188])).
% 102.50/66.13 tff(197,plain,
% 102.50/66.13 (![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))))))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[196, 186])).
% 102.50/66.13 tff(198,plain,
% 102.50/66.13 (((~![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))))))))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(199,plain,
% 102.50/66.13 ((~![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))))))))),
% 102.50/66.13 inference(quant_inst,[status(thm)],[])).
% 102.50/66.13 tff(200,plain,
% 102.50/66.13 ((~![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)))))))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[199, 198])).
% 102.50/66.13 tff(201,plain,
% 102.50/66.13 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 102.50/66.13 inference(unit_resolution,[status(thm)],[200, 35, 34, 33, 197])).
% 102.50/66.13 tff(202,plain,
% 102.50/66.13 (^[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))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(203,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[202])).
% 102.50/66.13 tff(204,plain,
% 102.50/66.13 (^[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)))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(205,plain,
% 102.50/66.13 (![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)))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[204])).
% 102.50/66.13 tff(206,plain,
% 102.50/66.13 (![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))),
% 102.50/66.13 inference(rewrite,[status(thm)],[])).
% 102.50/66.13 tff(207,plain,
% 102.50/66.13 (^[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))))),
% 102.50/66.13 inference(bind,[status(th)],[])).
% 102.50/66.13 tff(208,plain,
% 102.50/66.13 (![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))),
% 102.50/66.13 inference(quant_intro,[status(thm)],[207])).
% 102.50/66.13 tff(209,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','existence_m1_filter_0')).
% 102.50/66.13 tff(210,plain,
% 102.50/66.13 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[209, 208])).
% 102.50/66.13 tff(211,plain,
% 102.50/66.13 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 102.50/66.13 inference(modus_ponens,[status(thm)],[210, 206])).
% 102.50/66.13 tff(212,plain,(
% 102.50/66.14 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A))),
% 102.50/66.14 inference(skolemize,[status(sab)],[211])).
% 102.50/66.14 tff(213,plain,
% 102.50/66.14 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[212, 205])).
% 102.50/66.14 tff(214,plain,
% 102.50/66.14 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[213, 203])).
% 102.50/66.14 tff(215,plain,
% 102.50/66.14 (((~![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)) | (~v10_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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(216,plain,
% 102.50/66.14 ((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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(217,plain,
% 102.50/66.14 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0)))),
% 102.50/66.14 inference(monotonicity,[status(thm)],[216])).
% 102.50/66.14 tff(218,plain,
% 102.50/66.14 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 102.50/66.14 inference(transitivity,[status(thm)],[217, 215])).
% 102.50/66.14 tff(219,plain,
% 102.50/66.14 ((~![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)))),
% 102.50/66.14 inference(quant_inst,[status(thm)],[])).
% 102.50/66.14 tff(220,plain,
% 102.50/66.14 ((~![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)) | (~v10_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0)),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[219, 218])).
% 102.50/66.14 tff(221,plain,
% 102.50/66.14 (m1_filter_0(tptp_fun_B_7(A!0), A!0)),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[220, 35, 34, 33, 214])).
% 102.50/66.14 tff(222,plain,
% 102.50/66.14 (((~![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)))))))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(223,plain,
% 102.50/66.14 ((~![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)))))))),
% 102.50/66.14 inference(quant_inst,[status(thm)],[])).
% 102.50/66.14 tff(224,plain,
% 102.50/66.14 ((~![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))))))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[223, 222])).
% 102.50/66.14 tff(225,plain,
% 102.50/66.14 (~(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)))))),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[224, 221, 201])).
% 102.50/66.14 tff(226,plain,
% 102.50/66.14 ((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)))),
% 102.50/66.14 inference(tautology,[status(thm)],[])).
% 102.50/66.14 tff(227,plain,
% 102.50/66.14 (m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[226, 225])).
% 102.50/66.14 tff(228,plain,
% 102.50/66.14 ((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)))),
% 102.50/66.14 inference(tautology,[status(thm)],[])).
% 102.50/66.14 tff(229,plain,
% 102.50/66.14 (~v1_xboole_0(tptp_fun_B_7(A!0))),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[228, 225])).
% 102.50/66.14 tff(230,plain,
% 102.50/66.14 (^[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))))))),
% 102.50/66.14 inference(bind,[status(th)],[])).
% 102.50/66.14 tff(231,plain,
% 102.50/66.14 (![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)))))),
% 102.50/66.14 inference(quant_intro,[status(thm)],[230])).
% 102.50/66.14 tff(232,plain,
% 102.50/66.14 (^[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)))))))),
% 102.50/66.14 inference(bind,[status(th)],[])).
% 102.50/66.14 tff(233,plain,
% 102.50/66.14 (![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)))))),
% 102.50/66.14 inference(quant_intro,[status(thm)],[232])).
% 102.50/66.14 tff(234,plain,
% 102.50/66.14 (![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))))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(235,plain,
% 102.50/66.14 (^[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))))))),
% 102.50/66.14 inference(bind,[status(th)],[])).
% 102.50/66.14 tff(236,plain,
% 102.50/66.14 (![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))))),
% 102.50/66.14 inference(quant_intro,[status(thm)],[235])).
% 102.50/66.14 tff(237,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/sandbox/benchmark/theBenchmark.p','rc1_lattice4')).
% 102.50/66.14 tff(238,plain,
% 102.50/66.14 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[237, 236])).
% 102.50/66.14 tff(239,plain,
% 102.50/66.14 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[238, 234])).
% 102.50/66.14 tff(240,plain,(
% 102.50/66.14 ![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)))))),
% 102.50/66.14 inference(skolemize,[status(sab)],[239])).
% 102.50/66.14 tff(241,plain,
% 102.50/66.14 (![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)))))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[240, 233])).
% 102.50/66.14 tff(242,plain,
% 102.50/66.14 (![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)))))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[241, 231])).
% 102.50/66.14 tff(243,plain,
% 102.50/66.14 (((~![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)))))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(244,plain,
% 102.50/66.14 ((~![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)))))),
% 102.50/66.14 inference(quant_inst,[status(thm)],[])).
% 102.50/66.14 tff(245,plain,
% 102.50/66.14 ((~![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))))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[244, 243])).
% 102.50/66.14 tff(246,plain,
% 102.50/66.14 (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[245, 35, 34, 33, 242])).
% 102.50/66.14 tff(247,plain,
% 102.50/66.14 ((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)),
% 102.50/66.14 inference(tautology,[status(thm)],[])).
% 102.50/66.14 tff(248,plain,
% 102.50/66.14 (m2_lattice4(tptp_fun_B_19(A!0), A!0)),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[247, 246])).
% 102.50/66.14 tff(249,plain,
% 102.50/66.14 (((~![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))))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(250,plain,
% 102.50/66.14 ((~![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))))),
% 102.50/66.14 inference(quant_inst,[status(thm)],[])).
% 102.50/66.14 tff(251,plain,
% 102.50/66.14 ((~![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)))),
% 102.50/66.14 inference(modus_ponens,[status(thm)],[250, 249])).
% 102.50/66.14 tff(252,plain,
% 102.50/66.14 (m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[251, 248, 70])).
% 102.50/66.14 tff(253,plain,
% 102.50/66.14 ((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)))),
% 102.50/66.14 inference(tautology,[status(thm)],[])).
% 102.50/66.14 tff(254,plain,
% 102.50/66.14 (~v1_xboole_0(tptp_fun_B_19(A!0))),
% 102.50/66.14 inference(unit_resolution,[status(thm)],[253, 246])).
% 102.50/66.14 tff(255,plain,
% 102.50/66.14 (^[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)))))))))))),
% 102.50/66.14 inference(bind,[status(th)],[])).
% 102.50/66.14 tff(256,plain,
% 102.50/66.14 (![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))))))))))),
% 102.50/66.14 inference(quant_intro,[status(thm)],[255])).
% 102.50/66.14 tff(257,plain,
% 102.50/66.14 (^[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)))))))))))),
% 102.50/66.14 inference(bind,[status(th)],[])).
% 102.50/66.14 tff(258,plain,
% 102.50/66.14 (![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))))))))))),
% 102.50/66.14 inference(quant_intro,[status(thm)],[257])).
% 102.50/66.14 tff(259,plain,
% 102.50/66.14 (![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))))))))))),
% 102.50/66.14 inference(transitivity,[status(thm)],[258, 256])).
% 102.50/66.14 tff(260,plain,
% 102.50/66.14 (^[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))))))))))))),
% 102.50/66.14 inference(bind,[status(th)],[])).
% 102.50/66.14 tff(261,plain,
% 102.50/66.14 (![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))))))))))),
% 102.50/66.14 inference(quant_intro,[status(thm)],[260])).
% 102.50/66.14 tff(262,plain,
% 102.50/66.14 (![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))))))))),
% 102.50/66.14 inference(rewrite,[status(thm)],[])).
% 102.50/66.14 tff(263,plain,
% 102.50/66.14 (^[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))))))))))),
% 102.50/66.15 inference(bind,[status(th)],[])).
% 102.50/66.15 tff(264,plain,
% 102.50/66.15 (![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))))))))),
% 102.50/66.15 inference(quant_intro,[status(thm)],[263])).
% 102.50/66.15 tff(265,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/sandbox/benchmark/theBenchmark.p','t45_filter_2')).
% 102.50/66.15 tff(266,plain,
% 102.50/66.15 (![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))))))))),
% 102.50/66.15 inference(modus_ponens,[status(thm)],[265, 264])).
% 102.50/66.15 tff(267,plain,
% 102.50/66.15 (![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))))))))),
% 102.50/66.15 inference(modus_ponens,[status(thm)],[266, 262])).
% 102.50/66.15 tff(268,plain,(
% 102.50/66.15 ![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))))))))),
% 102.50/66.15 inference(skolemize,[status(sab)],[267])).
% 102.50/66.15 tff(269,plain,
% 102.50/66.15 (![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))))))))))),
% 102.50/66.15 inference(modus_ponens,[status(thm)],[268, 261])).
% 102.50/66.15 tff(270,plain,
% 102.50/66.15 (![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))))))))))),
% 102.50/66.15 inference(modus_ponens,[status(thm)],[269, 259])).
% 102.50/66.15 tff(271,plain,
% 102.50/66.15 (((~![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))))))))))),
% 102.50/66.15 inference(rewrite,[status(thm)],[])).
% 102.50/66.15 tff(272,plain,
% 102.50/66.15 ((~![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))))))))))),
% 102.50/66.15 inference(quant_inst,[status(thm)],[])).
% 102.50/66.15 tff(273,plain,
% 102.50/66.15 ((~![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)))))))))),
% 102.50/66.15 inference(modus_ponens,[status(thm)],[272, 271])).
% 102.50/66.15 tff(274,plain,
% 102.50/66.15 (![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)))))))))),
% 102.50/66.15 inference(unit_resolution,[status(thm)],[273, 35, 34, 33, 270])).
% 102.50/66.15 tff(275,plain,
% 102.50/66.15 (((~![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)))))))))),
% 102.50/66.15 inference(rewrite,[status(thm)],[])).
% 102.50/66.15 tff(276,plain,
% 102.50/66.15 ((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)))))))))),
% 102.50/66.15 inference(rewrite,[status(thm)],[])).
% 102.50/66.15 tff(277,plain,
% 102.50/66.15 (((~![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))))))))))),
% 102.50/66.15 inference(monotonicity,[status(thm)],[276])).
% 102.50/66.15 tff(278,plain,
% 102.50/66.15 (((~![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)))))))))),
% 102.50/66.16 inference(transitivity,[status(thm)],[277, 275])).
% 102.50/66.16 tff(279,plain,
% 102.50/66.16 ((~![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)))))))))),
% 102.50/66.16 inference(quant_inst,[status(thm)],[])).
% 102.50/66.16 tff(280,plain,
% 102.50/66.16 ((~![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))))))))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[279, 278])).
% 102.50/66.16 tff(281,plain,
% 102.50/66.16 ((~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))))))))),
% 102.50/66.16 inference(unit_resolution,[status(thm)],[280, 274, 254])).
% 102.50/66.16 tff(282,plain,
% 102.50/66.16 (![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))))))))),
% 102.50/66.16 inference(unit_resolution,[status(thm)],[281, 252])).
% 102.50/66.16 tff(283,plain,
% 102.50/66.16 (((~![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)))))))))),
% 102.50/66.16 inference(rewrite,[status(thm)],[])).
% 102.50/66.16 tff(284,plain,
% 102.50/66.16 ((~![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)))))))))),
% 102.50/66.16 inference(quant_inst,[status(thm)],[])).
% 102.50/66.16 tff(285,plain,
% 102.50/66.16 ((~![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))))))))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[284, 283])).
% 102.50/66.16 tff(286,plain,
% 102.50/66.16 (![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))))))))),
% 102.50/66.16 inference(unit_resolution,[status(thm)],[285, 282, 229, 227])).
% 102.50/66.16 tff(287,plain,
% 102.50/66.16 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | (~v1_xboole_0(B!1))),
% 102.50/66.16 inference(tautology,[status(thm)],[])).
% 102.50/66.16 tff(288,plain,
% 102.50/66.16 (~v1_xboole_0(B!1)),
% 102.50/66.16 inference(unit_resolution,[status(thm)],[287, 156])).
% 102.50/66.16 tff(289,plain,
% 102.50/66.16 (^[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))))),
% 102.50/66.16 inference(bind,[status(th)],[])).
% 102.50/66.16 tff(290,plain,
% 102.50/66.16 (![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)))),
% 102.50/66.16 inference(quant_intro,[status(thm)],[289])).
% 102.50/66.16 tff(291,plain,
% 102.50/66.16 (^[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)))))),
% 102.50/66.16 inference(bind,[status(th)],[])).
% 102.50/66.16 tff(292,plain,
% 102.50/66.16 (![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)))),
% 102.50/66.16 inference(quant_intro,[status(thm)],[291])).
% 102.50/66.16 tff(293,plain,
% 102.50/66.16 (![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))))))),
% 102.50/66.16 inference(rewrite,[status(thm)],[])).
% 102.50/66.16 tff(294,plain,
% 102.50/66.16 (^[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))))))))),
% 102.50/66.16 inference(bind,[status(th)],[])).
% 102.50/66.16 tff(295,plain,
% 102.50/66.16 (![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))))))),
% 102.50/66.16 inference(quant_intro,[status(thm)],[294])).
% 102.50/66.16 tff(296,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/sandbox/benchmark/theBenchmark.p','fc1_filter_2')).
% 102.50/66.16 tff(297,plain,
% 102.50/66.16 (![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))))))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[296, 295])).
% 102.50/66.16 tff(298,plain,
% 102.50/66.16 (![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))))))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[297, 293])).
% 102.50/66.16 tff(299,plain,(
% 102.50/66.16 ![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))))))),
% 102.50/66.16 inference(skolemize,[status(sab)],[298])).
% 102.50/66.16 tff(300,plain,
% 102.50/66.16 (![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)))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[299, 292])).
% 102.50/66.16 tff(301,plain,
% 102.50/66.16 (![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)))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[300, 290])).
% 102.50/66.16 tff(302,plain,
% 102.50/66.16 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 102.50/66.16 inference(rewrite,[status(thm)],[])).
% 102.50/66.16 tff(303,plain,
% 102.50/66.16 ((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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 102.50/66.16 inference(rewrite,[status(thm)],[])).
% 102.50/66.16 tff(304,plain,
% 102.50/66.16 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))))),
% 102.50/66.16 inference(monotonicity,[status(thm)],[303])).
% 102.50/66.16 tff(305,plain,
% 102.50/66.16 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 102.50/66.16 inference(transitivity,[status(thm)],[304, 302])).
% 102.50/66.16 tff(306,plain,
% 102.50/66.16 ((~![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)))),
% 102.50/66.16 inference(quant_inst,[status(thm)],[])).
% 102.50/66.16 tff(307,plain,
% 102.50/66.16 ((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))),
% 102.50/66.16 inference(modus_ponens,[status(thm)],[306, 305])).
% 102.50/66.16 tff(308,plain,
% 102.50/66.16 (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))),
% 102.50/66.16 inference(unit_resolution,[status(thm)],[307, 35, 34, 33, 301])).
% 102.50/66.16 tff(309,plain,
% 102.50/66.16 (~v1_xboole_0(k7_filter_2(A!0, B!1))),
% 102.50/66.16 inference(unit_resolution,[status(thm)],[308, 162, 288])).
% 102.50/66.16 tff(310,plain,
% 102.50/66.16 (((~![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)))))))),
% 102.50/66.16 inference(rewrite,[status(thm)],[])).
% 102.50/66.16 tff(311,plain,
% 102.50/66.16 ((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)))))))),
% 102.50/66.16 inference(rewrite,[status(thm)],[])).
% 102.50/66.16 tff(312,plain,
% 102.50/66.16 (((~![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))))))))),
% 102.50/66.17 inference(monotonicity,[status(thm)],[311])).
% 102.50/66.17 tff(313,plain,
% 102.50/66.17 (((~![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)))))))),
% 102.50/66.17 inference(transitivity,[status(thm)],[312, 310])).
% 102.50/66.17 tff(314,plain,
% 102.50/66.17 ((~![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))))))))),
% 102.50/66.17 inference(quant_inst,[status(thm)],[])).
% 102.50/66.17 tff(315,plain,
% 102.50/66.17 ((~![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))))))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[314, 313])).
% 102.50/66.17 tff(316,plain,
% 102.50/66.17 (![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))))))),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[315, 175, 309, 286])).
% 102.50/66.17 tff(317,plain,
% 102.50/66.17 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | (~v1_xboole_0(C!2))),
% 102.50/66.17 inference(tautology,[status(thm)],[])).
% 102.50/66.17 tff(318,plain,
% 102.50/66.17 (~v1_xboole_0(C!2)),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[317, 45])).
% 102.50/66.17 tff(319,plain,
% 102.50/66.17 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 102.50/66.17 inference(rewrite,[status(thm)],[])).
% 102.50/66.17 tff(320,plain,
% 102.50/66.17 ((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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 102.50/66.17 inference(rewrite,[status(thm)],[])).
% 102.50/66.17 tff(321,plain,
% 102.50/66.17 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))))),
% 102.50/66.17 inference(monotonicity,[status(thm)],[320])).
% 102.50/66.17 tff(322,plain,
% 102.50/66.17 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 102.50/66.17 inference(transitivity,[status(thm)],[321, 319])).
% 102.50/66.17 tff(323,plain,
% 102.50/66.17 ((~![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)))),
% 102.50/66.17 inference(quant_inst,[status(thm)],[])).
% 102.50/66.17 tff(324,plain,
% 102.50/66.17 ((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[323, 322])).
% 102.50/66.17 tff(325,plain,
% 102.50/66.17 (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[324, 35, 34, 33, 301])).
% 102.50/66.17 tff(326,plain,
% 102.50/66.17 (~v1_xboole_0(k7_filter_2(A!0, C!2))),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[325, 74, 318])).
% 102.50/66.17 tff(327,plain,
% 102.50/66.17 (((~![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)))))))),
% 102.50/66.17 inference(rewrite,[status(thm)],[])).
% 102.50/66.17 tff(328,plain,
% 102.50/66.17 ((~![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)))))))),
% 102.50/66.17 inference(quant_inst,[status(thm)],[])).
% 102.50/66.17 tff(329,plain,
% 102.50/66.17 ((~![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))))))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[328, 327])).
% 102.50/66.17 tff(330,plain,
% 102.50/66.17 (~((~(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)))))),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[329, 123, 326, 316])).
% 102.50/66.17 tff(331,plain,
% 102.50/66.17 (((~(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)))),
% 102.50/66.17 inference(tautology,[status(thm)],[])).
% 102.50/66.17 tff(332,plain,
% 102.50/66.17 (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))),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[331, 330])).
% 102.50/66.17 tff(333,plain,
% 102.50/66.17 (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)))),
% 102.50/66.17 inference(symmetry,[status(thm)],[332])).
% 102.50/66.17 tff(334,plain,
% 102.50/66.17 (^[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)))))),
% 102.50/66.17 inference(bind,[status(th)],[])).
% 102.50/66.17 tff(335,plain,
% 102.50/66.17 (![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))))),
% 102.50/66.17 inference(quant_intro,[status(thm)],[334])).
% 102.50/66.17 tff(336,plain,
% 102.50/66.17 (![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))))),
% 102.50/66.17 inference(rewrite,[status(thm)],[])).
% 102.50/66.17 tff(337,plain,
% 102.50/66.17 (^[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)))))),
% 102.50/66.17 inference(bind,[status(th)],[])).
% 102.50/66.17 tff(338,plain,
% 102.50/66.17 (![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))))),
% 102.50/66.17 inference(quant_intro,[status(thm)],[337])).
% 102.50/66.17 tff(339,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 102.50/66.17 tff(340,plain,
% 102.50/66.17 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[339, 338])).
% 102.50/66.17 tff(341,plain,
% 102.50/66.17 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[340, 336])).
% 102.50/66.17 tff(342,plain,(
% 102.50/66.17 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 102.50/66.17 inference(skolemize,[status(sab)],[341])).
% 102.50/66.17 tff(343,plain,
% 102.50/66.17 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[342, 335])).
% 102.50/66.17 tff(344,plain,
% 102.50/66.17 (((~![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))))),
% 102.50/66.17 inference(rewrite,[status(thm)],[])).
% 102.50/66.17 tff(345,plain,
% 102.50/66.17 ((~![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))))),
% 102.50/66.17 inference(quant_inst,[status(thm)],[])).
% 102.50/66.17 tff(346,plain,
% 102.50/66.17 ((~![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)))),
% 102.50/66.17 inference(modus_ponens,[status(thm)],[345, 344])).
% 102.50/66.17 tff(347,plain,
% 102.50/66.17 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 102.50/66.17 inference(unit_resolution,[status(thm)],[346, 33, 343])).
% 102.50/66.17 tff(348,plain,
% 102.50/66.17 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 102.50/66.17 inference(symmetry,[status(thm)],[347])).
% 102.50/66.17 tff(349,plain,
% 102.50/66.17 (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))),
% 102.50/66.17 inference(monotonicity,[status(thm)],[348])).
% 102.50/66.17 tff(350,plain,
% 102.50/66.17 (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)),
% 102.50/66.17 inference(transitivity,[status(thm)],[349, 333, 181])).
% 102.50/66.17 tff(351,plain,
% 102.50/66.17 (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))),
% 102.50/66.17 inference(monotonicity,[status(thm)],[167, 350])).
% 102.50/66.17 tff(352,plain,
% 102.50/66.17 (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))),
% 102.50/66.17 inference(monotonicity,[status(thm)],[348])).
% 102.50/66.17 tff(353,plain,
% 102.50/66.17 (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)))),
% 102.50/66.17 inference(symmetry,[status(thm)],[352])).
% 102.50/66.17 tff(354,plain,
% 102.50/66.17 ((~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))))),
% 102.50/66.17 inference(monotonicity,[status(thm)],[353])).
% 102.50/66.17 tff(355,plain,
% 102.50/66.17 (^[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)))))))),
% 102.50/66.17 inference(bind,[status(th)],[])).
% 102.50/66.17 tff(356,plain,
% 102.50/66.17 (![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))))))),
% 102.50/66.17 inference(quant_intro,[status(thm)],[355])).
% 102.50/66.17 tff(357,plain,
% 102.50/66.17 (^[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))))))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(358,plain,
% 102.50/66.18 (![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))))))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[357])).
% 102.50/66.18 tff(359,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(360,plain,
% 102.50/66.18 (^[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))))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(361,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[360])).
% 102.50/66.18 tff(362,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 102.50/66.18 tff(363,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[362, 361])).
% 102.50/66.18 tff(364,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[363, 359])).
% 102.50/66.18 tff(365,plain,(
% 102.50/66.18 ![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))))),
% 102.50/66.18 inference(skolemize,[status(sab)],[364])).
% 102.50/66.18 tff(366,plain,
% 102.50/66.18 (![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))))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[365, 358])).
% 102.50/66.18 tff(367,plain,
% 102.50/66.18 (![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))))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[366, 356])).
% 102.50/66.18 tff(368,plain,
% 102.50/66.18 (((~![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))))))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(369,plain,
% 102.50/66.18 ((~![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))))))),
% 102.50/66.18 inference(quant_inst,[status(thm)],[])).
% 102.50/66.18 tff(370,plain,
% 102.50/66.18 ((~![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)))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[369, 368])).
% 102.50/66.18 tff(371,plain,
% 102.50/66.18 (~(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))))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[370, 35, 34, 33, 367])).
% 102.50/66.18 tff(372,plain,
% 102.50/66.18 ((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)))),
% 102.50/66.18 inference(tautology,[status(thm)],[])).
% 102.50/66.18 tff(373,plain,
% 102.50/66.18 (~v3_struct_0(k1_lattice2(A!0))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[372, 371])).
% 102.50/66.18 tff(374,plain,
% 102.50/66.18 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[373, 354])).
% 102.50/66.18 tff(375,plain,
% 102.50/66.18 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 102.50/66.18 inference(monotonicity,[status(thm)],[348])).
% 102.50/66.18 tff(376,plain,
% 102.50/66.18 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 102.50/66.18 inference(symmetry,[status(thm)],[375])).
% 102.50/66.18 tff(377,plain,
% 102.50/66.18 ((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))),
% 102.50/66.18 inference(tautology,[status(thm)],[])).
% 102.50/66.18 tff(378,plain,
% 102.50/66.18 (v10_lattices(k1_lattice2(A!0))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[377, 371])).
% 102.50/66.18 tff(379,plain,
% 102.50/66.18 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[378, 376])).
% 102.50/66.18 tff(380,plain,
% 102.50/66.18 (l3_lattices(k1_lattice2(A!0)) <=> l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 102.50/66.18 inference(monotonicity,[status(thm)],[347])).
% 102.50/66.18 tff(381,plain,
% 102.50/66.18 (^[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)))))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(382,plain,
% 102.50/66.18 (![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))))))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[381])).
% 102.50/66.18 tff(383,plain,
% 102.50/66.18 (^[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)))))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(384,plain,
% 102.50/66.18 (![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))))))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[383])).
% 102.50/66.18 tff(385,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(386,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(387,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[386])).
% 102.50/66.18 tff(388,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lattice2')).
% 102.50/66.18 tff(389,plain,
% 102.50/66.18 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[388, 387])).
% 102.50/66.18 tff(390,plain,
% 102.50/66.18 (![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[389, 385])).
% 102.50/66.18 tff(391,plain,(
% 102.50/66.18 ![A: $i] : ((~l3_lattices(A)) | (v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A))))),
% 102.50/66.18 inference(skolemize,[status(sab)],[390])).
% 102.50/66.18 tff(392,plain,
% 102.50/66.18 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[391, 384])).
% 102.50/66.18 tff(393,plain,
% 102.50/66.18 (![A: $i] : ((~l3_lattices(A)) | (~((~v3_lattices(k1_lattice2(A))) | (~l3_lattices(k1_lattice2(A))))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[392, 382])).
% 102.50/66.18 tff(394,plain,
% 102.50/66.18 (((~![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))))))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(395,plain,
% 102.50/66.18 ((~![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))))))),
% 102.50/66.18 inference(quant_inst,[status(thm)],[])).
% 102.50/66.18 tff(396,plain,
% 102.50/66.18 ((~![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)))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[395, 394])).
% 102.50/66.18 tff(397,plain,
% 102.50/66.18 (~((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0))))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[396, 33, 393])).
% 102.50/66.18 tff(398,plain,
% 102.50/66.18 (((~v3_lattices(k1_lattice2(A!0))) | (~l3_lattices(k1_lattice2(A!0)))) | l3_lattices(k1_lattice2(A!0))),
% 102.50/66.18 inference(tautology,[status(thm)],[])).
% 102.50/66.18 tff(399,plain,
% 102.50/66.18 (l3_lattices(k1_lattice2(A!0))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[398, 397])).
% 102.50/66.18 tff(400,plain,
% 102.50/66.18 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[399, 380])).
% 102.50/66.18 tff(401,plain,
% 102.50/66.18 (^[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))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(402,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[401])).
% 102.50/66.18 tff(403,plain,
% 102.50/66.18 (^[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))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(404,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[403])).
% 102.50/66.18 tff(405,plain,
% 102.50/66.18 (^[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))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(406,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[405])).
% 102.50/66.18 tff(407,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(transitivity,[status(thm)],[406, 404])).
% 102.50/66.18 tff(408,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(409,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[408])).
% 102.50/66.18 tff(410,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(411,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(412,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[411])).
% 102.50/66.18 tff(413,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 102.50/66.18 tff(414,plain,
% 102.50/66.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[413, 412])).
% 102.50/66.18 tff(415,plain,
% 102.50/66.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[414, 410])).
% 102.50/66.18 tff(416,plain,(
% 102.50/66.18 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 102.50/66.18 inference(skolemize,[status(sab)],[415])).
% 102.50/66.18 tff(417,plain,
% 102.50/66.18 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[416, 409])).
% 102.50/66.18 tff(418,plain,
% 102.50/66.18 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[417, 407])).
% 102.50/66.18 tff(419,plain,
% 102.50/66.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[418, 402])).
% 102.50/66.18 tff(420,plain,
% 102.50/66.18 (((~![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)))))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(421,plain,
% 102.50/66.18 ((~![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)))))),
% 102.50/66.18 inference(quant_inst,[status(thm)],[])).
% 102.50/66.18 tff(422,plain,
% 102.50/66.18 ((~![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))))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[421, 420])).
% 102.50/66.18 tff(423,plain,
% 102.50/66.18 (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))))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[422, 419])).
% 102.50/66.18 tff(424,plain,
% 102.50/66.18 (![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))))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[423, 400, 379, 374])).
% 102.50/66.18 tff(425,plain,
% 102.50/66.18 ((~![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))))),
% 102.50/66.18 inference(quant_inst,[status(thm)],[])).
% 102.50/66.18 tff(426,plain,
% 102.50/66.18 (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)))),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[425, 424])).
% 102.50/66.18 tff(427,plain,
% 102.50/66.18 (^[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))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(428,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[427])).
% 102.50/66.18 tff(429,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(430,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[429])).
% 102.50/66.18 tff(431,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(432,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(433,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[432])).
% 102.50/66.18 tff(434,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 102.50/66.18 tff(435,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[434, 433])).
% 102.50/66.18 tff(436,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[435, 431])).
% 102.50/66.18 tff(437,plain,(
% 102.50/66.18 ![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)))),
% 102.50/66.18 inference(skolemize,[status(sab)],[436])).
% 102.50/66.18 tff(438,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[437, 430])).
% 102.50/66.18 tff(439,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[438, 428])).
% 102.50/66.18 tff(440,plain,
% 102.50/66.18 (((~![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)))) | ((~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(441,plain,
% 102.50/66.18 ((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))) <=> ((~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(442,plain,
% 102.50/66.18 (((~![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)))) | ((~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))))),
% 102.50/66.18 inference(monotonicity,[status(thm)],[441])).
% 102.50/66.18 tff(443,plain,
% 102.50/66.18 (((~![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)))) | (~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 102.50/66.18 inference(transitivity,[status(thm)],[442, 440])).
% 102.50/66.18 tff(444,plain,
% 102.50/66.18 ((~![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)))),
% 102.50/66.18 inference(quant_inst,[status(thm)],[])).
% 102.50/66.18 tff(445,plain,
% 102.50/66.18 ((~![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)))) | (~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[444, 443])).
% 102.50/66.18 tff(446,plain,
% 102.50/66.18 (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)),
% 102.50/66.18 inference(unit_resolution,[status(thm)],[445, 35, 34, 33, 152, 439])).
% 102.50/66.18 tff(447,plain,
% 102.50/66.18 (k7_filter_2(A!0, B!1) = k15_filter_2(A!0, B!1)),
% 102.50/66.18 inference(symmetry,[status(thm)],[446])).
% 102.50/66.18 tff(448,plain,
% 102.50/66.18 (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))),
% 102.50/66.18 inference(monotonicity,[status(thm)],[447, 348])).
% 102.50/66.18 tff(449,plain,
% 102.50/66.18 (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)))),
% 102.50/66.18 inference(symmetry,[status(thm)],[448])).
% 102.50/66.18 tff(450,plain,
% 102.50/66.18 (^[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))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(451,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[450])).
% 102.50/66.18 tff(452,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(453,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[452])).
% 102.50/66.18 tff(454,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(rewrite,[status(thm)],[])).
% 102.50/66.18 tff(455,plain,
% 102.50/66.18 (^[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)))))),
% 102.50/66.18 inference(bind,[status(th)],[])).
% 102.50/66.18 tff(456,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(quant_intro,[status(thm)],[455])).
% 102.50/66.18 tff(457,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k15_filter_2')).
% 102.50/66.18 tff(458,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[457, 456])).
% 102.50/66.18 tff(459,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[458, 454])).
% 102.50/66.18 tff(460,plain,(
% 102.50/66.18 ![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)))),
% 102.50/66.18 inference(skolemize,[status(sab)],[459])).
% 102.50/66.18 tff(461,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[460, 453])).
% 102.50/66.18 tff(462,plain,
% 102.50/66.18 (![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)))),
% 102.50/66.18 inference(modus_ponens,[status(thm)],[461, 451])).
% 102.50/66.18 tff(463,plain,
% 102.50/66.18 (((~![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)))) | ((~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (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)))) | (~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(464,plain,
% 102.50/66.19 ((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))) <=> ((~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(465,plain,
% 102.50/66.19 (((~![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)))) | ((~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 102.50/66.19 inference(monotonicity,[status(thm)],[464])).
% 102.50/66.19 tff(466,plain,
% 102.50/66.19 (((~![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)))) | (~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 102.50/66.19 inference(transitivity,[status(thm)],[465, 463])).
% 102.50/66.19 tff(467,plain,
% 102.50/66.19 ((~![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)))),
% 102.50/66.19 inference(quant_inst,[status(thm)],[])).
% 102.50/66.19 tff(468,plain,
% 102.50/66.19 ((~![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)))) | (~m2_filter_2(B!1, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[467, 466])).
% 102.50/66.19 tff(469,plain,
% 102.50/66.19 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[468, 35, 34, 33, 152, 462])).
% 102.50/66.19 tff(470,plain,
% 102.50/66.19 (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)))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[469, 449])).
% 102.50/66.19 tff(471,plain,
% 102.50/66.19 ((~(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)))),
% 102.50/66.19 inference(tautology,[status(thm)],[])).
% 102.50/66.19 tff(472,plain,
% 102.50/66.19 (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)))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[471, 470, 426])).
% 102.50/66.19 tff(473,plain,
% 102.50/66.19 (^[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)))))))))),
% 102.50/66.19 inference(bind,[status(th)],[])).
% 102.50/66.19 tff(474,plain,
% 102.50/66.19 (![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))))))))),
% 102.50/66.19 inference(quant_intro,[status(thm)],[473])).
% 102.50/66.19 tff(475,plain,
% 102.50/66.19 (^[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)))))))))),
% 102.50/66.19 inference(bind,[status(th)],[])).
% 102.50/66.19 tff(476,plain,
% 102.50/66.19 (![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))))))))),
% 102.50/66.19 inference(quant_intro,[status(thm)],[475])).
% 102.50/66.19 tff(477,plain,
% 102.50/66.19 (![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))))))))),
% 102.50/66.19 inference(transitivity,[status(thm)],[476, 474])).
% 102.50/66.19 tff(478,plain,
% 102.50/66.19 (^[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))))))))))),
% 102.50/66.19 inference(bind,[status(th)],[])).
% 102.50/66.19 tff(479,plain,
% 102.50/66.19 (![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))))))))),
% 102.50/66.19 inference(quant_intro,[status(thm)],[478])).
% 102.50/66.19 tff(480,plain,
% 102.50/66.19 (![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))))))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(481,plain,
% 102.50/66.19 (^[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))))))))),
% 102.50/66.19 inference(bind,[status(th)],[])).
% 102.50/66.19 tff(482,plain,
% 102.50/66.19 (![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))))))),
% 102.50/66.19 inference(quant_intro,[status(thm)],[481])).
% 102.50/66.19 tff(483,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/sandbox/benchmark/theBenchmark.p','t49_filter_0')).
% 102.50/66.19 tff(484,plain,
% 102.50/66.19 (![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))))))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[483, 482])).
% 102.50/66.19 tff(485,plain,
% 102.50/66.19 (![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))))))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[484, 480])).
% 102.50/66.19 tff(486,plain,(
% 102.50/66.19 ![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))))))),
% 102.50/66.19 inference(skolemize,[status(sab)],[485])).
% 102.50/66.19 tff(487,plain,
% 102.50/66.19 (![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))))))))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[486, 479])).
% 102.50/66.19 tff(488,plain,
% 102.50/66.19 (![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))))))))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[487, 477])).
% 102.50/66.19 tff(489,plain,
% 102.50/66.19 (((~![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))))))))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(490,plain,
% 102.50/66.19 ((~![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))))))))),
% 102.50/66.19 inference(quant_inst,[status(thm)],[])).
% 102.50/66.19 tff(491,plain,
% 102.50/66.19 ((~![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)))))))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[490, 489])).
% 102.50/66.19 tff(492,plain,
% 102.50/66.19 (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)))))))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[491, 488])).
% 102.50/66.19 tff(493,plain,
% 102.50/66.19 (![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)))))))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[492, 400, 379, 374])).
% 102.50/66.19 tff(494,plain,
% 102.50/66.19 (((~![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)))))))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(495,plain,
% 102.50/66.19 ((~![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)))))))),
% 102.50/66.19 inference(quant_inst,[status(thm)],[])).
% 102.50/66.19 tff(496,plain,
% 102.50/66.19 ((~![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))))))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[495, 494])).
% 102.50/66.19 tff(497,plain,
% 102.50/66.19 ((~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))))))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[496, 493])).
% 102.50/66.19 tff(498,plain,
% 102.50/66.19 (![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))))))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[497, 472])).
% 102.50/66.19 tff(499,plain,
% 102.50/66.19 ((~![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))))),
% 102.50/66.19 inference(quant_inst,[status(thm)],[])).
% 102.50/66.19 tff(500,plain,
% 102.50/66.19 (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)))),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[499, 424])).
% 102.50/66.19 tff(501,plain,
% 102.50/66.19 (((~![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)))) | ((~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_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)))) | (~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(502,plain,
% 102.50/66.19 ((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))) <=> ((~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(503,plain,
% 102.50/66.19 (((~![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)))) | ((~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2))))),
% 102.50/66.19 inference(monotonicity,[status(thm)],[502])).
% 102.50/66.19 tff(504,plain,
% 102.50/66.19 (((~![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)))) | (~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 102.50/66.19 inference(transitivity,[status(thm)],[503, 501])).
% 102.50/66.19 tff(505,plain,
% 102.50/66.19 ((~![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)))),
% 102.50/66.19 inference(quant_inst,[status(thm)],[])).
% 102.50/66.19 tff(506,plain,
% 102.50/66.19 ((~![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)))) | (~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[505, 504])).
% 102.50/66.19 tff(507,plain,
% 102.50/66.19 (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)),
% 102.50/66.19 inference(unit_resolution,[status(thm)],[506, 35, 34, 33, 41, 439])).
% 102.50/66.19 tff(508,plain,
% 102.50/66.19 (k7_filter_2(A!0, C!2) = k15_filter_2(A!0, C!2)),
% 102.50/66.19 inference(symmetry,[status(thm)],[507])).
% 102.50/66.19 tff(509,plain,
% 102.50/66.19 (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))),
% 102.50/66.19 inference(monotonicity,[status(thm)],[508, 348])).
% 102.50/66.19 tff(510,plain,
% 102.50/66.19 (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)))),
% 102.50/66.19 inference(symmetry,[status(thm)],[509])).
% 102.50/66.19 tff(511,plain,
% 102.50/66.19 (((~![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)))) | ((~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_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)))) | (~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(512,plain,
% 102.50/66.19 ((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))) <=> ((~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 102.50/66.19 inference(rewrite,[status(thm)],[])).
% 102.50/66.19 tff(513,plain,
% 102.50/66.19 (((~![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)))) | ((~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))))),
% 102.50/66.19 inference(monotonicity,[status(thm)],[512])).
% 102.50/66.19 tff(514,plain,
% 102.50/66.19 (((~![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)))) | (~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 102.50/66.19 inference(transitivity,[status(thm)],[513, 511])).
% 102.50/66.19 tff(515,plain,
% 102.50/66.19 ((~![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)))),
% 102.50/66.19 inference(quant_inst,[status(thm)],[])).
% 102.50/66.19 tff(516,plain,
% 102.50/66.19 ((~![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)))) | (~m2_filter_2(C!2, A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 102.50/66.19 inference(modus_ponens,[status(thm)],[515, 514])).
% 102.50/66.19 tff(517,plain,
% 102.50/66.19 (m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 102.50/66.20 inference(unit_resolution,[status(thm)],[516, 35, 34, 33, 41, 462])).
% 102.50/66.20 tff(518,plain,
% 102.50/66.20 (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)))),
% 102.50/66.20 inference(modus_ponens,[status(thm)],[517, 510])).
% 102.50/66.20 tff(519,plain,
% 102.50/66.20 ((~(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)))),
% 102.50/66.20 inference(tautology,[status(thm)],[])).
% 102.50/66.20 tff(520,plain,
% 102.50/66.20 (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)))),
% 102.50/66.20 inference(unit_resolution,[status(thm)],[519, 518, 500])).
% 102.50/66.20 tff(521,plain,
% 102.50/66.20 (((~![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)))))))),
% 102.50/66.20 inference(rewrite,[status(thm)],[])).
% 102.50/66.20 tff(522,plain,
% 102.50/66.20 ((~![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)))))))),
% 102.50/66.20 inference(quant_inst,[status(thm)],[])).
% 102.50/66.20 tff(523,plain,
% 102.50/66.20 ((~![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))))))),
% 102.50/66.20 inference(modus_ponens,[status(thm)],[522, 521])).
% 102.50/66.20 tff(524,plain,
% 102.50/66.20 (~((~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)))))),
% 102.50/66.20 inference(unit_resolution,[status(thm)],[523, 520, 498])).
% 102.50/66.20 tff(525,plain,
% 102.50/66.20 (((~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)))),
% 102.50/66.20 inference(tautology,[status(thm)],[])).
% 102.50/66.20 tff(526,plain,
% 102.50/66.20 (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)))),
% 102.50/66.20 inference(unit_resolution,[status(thm)],[525, 524])).
% 102.50/66.20 tff(527,plain,
% 102.50/66.20 (r1_tarski(B!1, k20_filter_2(A!0, B!1, C!2))),
% 102.50/66.20 inference(modus_ponens,[status(thm)],[526, 351])).
% 102.50/66.20 tff(528,plain,
% 102.50/66.20 (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))),
% 102.50/66.20 inference(monotonicity,[status(thm)],[102, 350])).
% 102.50/66.20 tff(529,plain,
% 102.50/66.20 (((~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)))),
% 102.50/66.20 inference(tautology,[status(thm)],[])).
% 102.50/66.20 tff(530,plain,
% 102.50/66.20 (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)))),
% 102.50/66.20 inference(unit_resolution,[status(thm)],[529, 524])).
% 102.50/66.20 tff(531,plain,
% 102.50/66.20 (r1_tarski(C!2, k20_filter_2(A!0, B!1, C!2))),
% 102.50/66.20 inference(modus_ponens,[status(thm)],[530, 528])).
% 102.50/66.20 tff(532,plain,
% 102.50/66.20 ((~(~((~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))))),
% 102.50/66.20 inference(rewrite,[status(thm)],[])).
% 102.50/66.20 tff(533,plain,
% 102.50/66.20 ((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)))))),
% 102.50/66.20 inference(rewrite,[status(thm)],[])).
% 102.50/66.20 tff(534,plain,
% 102.50/66.20 ((~(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))))))),
% 102.50/66.20 inference(monotonicity,[status(thm)],[533])).
% 102.50/66.20 tff(535,plain,
% 102.50/66.20 ((~(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))))),
% 102.50/66.20 inference(transitivity,[status(thm)],[534, 532])).
% 102.50/66.20 tff(536,plain,
% 102.50/66.20 (~(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)))),
% 102.50/66.20 inference(or_elim,[status(thm)],[40])).
% 102.50/66.20 tff(537,plain,
% 102.64/66.27 ((~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)))),
% 102.64/66.27 inference(modus_ponens,[status(thm)],[536, 535])).
% 102.64/66.27 tff(538,plain,
% 102.64/66.27 ($false),
% 102.64/66.27 inference(unit_resolution,[status(thm)],[537, 531, 527])).
% 102.64/66.27 % SZS output end Proof
%------------------------------------------------------------------------------