TSTP Solution File: LAT337+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT337+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 18:33:13 EDT 2022
% Result : Theorem 0.20s 0.58s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT337+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 14:57:32 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 tff(v1_xboole_0_type, type, (
% 0.20/0.58 v1_xboole_0: $i > $o)).
% 0.20/0.58 tff(k22_filter_2_type, type, (
% 0.20/0.58 k22_filter_2: ( $i * $i * $i ) > $i)).
% 0.20/0.58 tff(tptp_fun_C_2_type, type, (
% 0.20/0.58 tptp_fun_C_2: $i)).
% 0.20/0.58 tff(tptp_fun_B_1_type, type, (
% 0.20/0.58 tptp_fun_B_1: $i)).
% 0.20/0.58 tff(tptp_fun_A_0_type, type, (
% 0.20/0.58 tptp_fun_A_0: $i)).
% 0.20/0.58 tff(m2_lattice4_type, type, (
% 0.20/0.58 m2_lattice4: ( $i * $i ) > $o)).
% 0.20/0.58 tff(m1_subset_1_type, type, (
% 0.20/0.58 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.58 tff(u1_struct_0_type, type, (
% 0.20/0.58 u1_struct_0: $i > $i)).
% 0.20/0.58 tff(l3_lattices_type, type, (
% 0.20/0.58 l3_lattices: $i > $o)).
% 0.20/0.58 tff(v10_lattices_type, type, (
% 0.20/0.58 v10_lattices: $i > $o)).
% 0.20/0.58 tff(v3_struct_0_type, type, (
% 0.20/0.58 v3_struct_0: $i > $o)).
% 0.20/0.58 tff(r3_lattices_type, type, (
% 0.20/0.58 r3_lattices: ( $i * $i * $i ) > $o)).
% 0.20/0.58 tff(v17_lattices_type, type, (
% 0.20/0.58 v17_lattices: $i > $o)).
% 0.20/0.58 tff(k23_filter_2_type, type, (
% 0.20/0.58 k23_filter_2: ( $i * $i ) > $i)).
% 0.20/0.58 tff(v11_lattices_type, type, (
% 0.20/0.58 v11_lattices: $i > $o)).
% 0.20/0.58 tff(v16_lattices_type, type, (
% 0.20/0.58 v16_lattices: $i > $o)).
% 0.20/0.58 tff(v15_lattices_type, type, (
% 0.20/0.58 v15_lattices: $i > $o)).
% 0.20/0.58 tff(v12_lattices_type, type, (
% 0.20/0.58 v12_lattices: $i > $o)).
% 0.20/0.58 tff(v14_lattices_type, type, (
% 0.20/0.58 v14_lattices: $i > $o)).
% 0.20/0.58 tff(v13_lattices_type, type, (
% 0.20/0.58 v13_lattices: $i > $o)).
% 0.20/0.58 tff(v9_lattices_type, type, (
% 0.20/0.58 v9_lattices: $i > $o)).
% 0.20/0.58 tff(v8_lattices_type, type, (
% 0.20/0.58 v8_lattices: $i > $o)).
% 0.20/0.58 tff(v4_lattices_type, type, (
% 0.20/0.58 v4_lattices: $i > $o)).
% 0.20/0.58 tff(v5_lattices_type, type, (
% 0.20/0.58 v5_lattices: $i > $o)).
% 0.20/0.58 tff(v6_lattices_type, type, (
% 0.20/0.58 v6_lattices: $i > $o)).
% 0.20/0.58 tff(v7_lattices_type, type, (
% 0.20/0.58 v7_lattices: $i > $o)).
% 0.20/0.58 tff(1,plain,
% 0.20/0.58 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(2,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.58 tff(3,plain,
% 0.20/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), rewrite(((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)) <=> (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(4,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.58 tff(5,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(6,plain,
% 0.20/0.58 (^[A: $i, B: $i, C: $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)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(7,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.58 tff(8,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k22_filter_2')).
% 0.20/0.58 tff(9,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.58 tff(10,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.58 tff(11,plain,(
% 0.20/0.58 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 0.20/0.58 inference(skolemize,[status(sab)],[10])).
% 0.20/0.58 tff(12,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.58 tff(13,plain,
% 0.20/0.58 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.58 tff(14,plain,
% 0.20/0.58 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(15,plain,
% 0.20/0.58 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(16,plain,
% 0.20/0.58 ((~(~((~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))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(17,plain,
% 0.20/0.58 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[16, 15])).
% 0.20/0.58 tff(18,plain,
% 0.20/0.58 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[17, 14])).
% 0.20/0.58 tff(19,plain,
% 0.20/0.58 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(20,plain,
% 0.20/0.58 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) & r3_lattices(A, B, C)) => ((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A)))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(21,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) & r3_lattices(A, B, C)) => ((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t87_filter_2')).
% 0.20/0.58 tff(22,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.58 tff(23,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.20/0.58 tff(24,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.58 tff(25,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.20/0.58 tff(26,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.20/0.58 tff(27,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.20/0.58 tff(28,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v17_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A, B, C))) | (~m1_subset_1(C, u1_struct_0(A))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.20/0.58 tff(29,plain,
% 0.20/0.58 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.58 tff(30,plain,
% 0.20/0.58 (~(((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 0.20/0.58 inference(and_elim,[status(thm)],[29])).
% 0.20/0.58 tff(31,plain,
% 0.20/0.58 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.20/0.58 inference(or_elim,[status(thm)],[30])).
% 0.20/0.58 tff(32,plain,
% 0.20/0.58 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.20/0.58 inference(and_elim,[status(thm)],[29])).
% 0.20/0.58 tff(33,plain,
% 0.20/0.58 (l3_lattices(A!0)),
% 0.20/0.58 inference(and_elim,[status(thm)],[29])).
% 0.20/0.58 tff(34,plain,
% 0.20/0.58 (v10_lattices(A!0)),
% 0.20/0.58 inference(and_elim,[status(thm)],[29])).
% 0.20/0.58 tff(35,plain,
% 0.20/0.58 (~v3_struct_0(A!0)),
% 0.20/0.58 inference(and_elim,[status(thm)],[29])).
% 0.20/0.58 tff(36,plain,
% 0.20/0.58 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(37,plain,
% 0.20/0.58 ((v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(38,plain,
% 0.20/0.58 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.58 tff(39,plain,
% 0.20/0.58 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.58 tff(40,plain,
% 0.20/0.58 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(41,plain,
% 0.20/0.58 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.58 tff(42,plain,
% 0.20/0.58 (~(v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[41, 35, 34, 33, 32, 31, 13])).
% 0.20/0.58 tff(43,plain,
% 0.20/0.58 ((v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))) | (~v1_xboole_0(k22_filter_2(A!0, B!1, C!2)))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(44,plain,
% 0.20/0.58 (~v1_xboole_0(k22_filter_2(A!0, B!1, C!2))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.58 tff(45,plain,
% 0.20/0.58 ((v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))) | m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(46,plain,
% 0.20/0.58 (m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[45, 42])).
% 0.20/0.58 tff(47,plain,
% 0.20/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(48,plain,
% 0.20/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.58 tff(49,plain,
% 0.20/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(50,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.59 tff(51,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.59 tff(52,plain,
% 0.20/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(53,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.59 tff(54,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(55,plain,
% 0.20/0.59 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) & v12_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) & v12_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A)))), ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A)) & r3_lattices(A, B, C)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A)) & r3_lattices(A, B, C)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))), ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))), trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))), (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))), rewrite((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))), (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))), ((((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> (((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))), rewrite((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))), ((((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) <=> ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))), (((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)) => ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)) => ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))), (((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))), ((m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))), ((m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(56,plain,
% 0.20/0.59 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.59 tff(57,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) & v12_lattices(A)) & r3_lattices(A, B, C)) => (((((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t86_filter_2')).
% 0.20/0.59 tff(58,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.59 tff(59,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.59 tff(60,plain,(
% 0.20/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((~v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C)))) & v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C))) & l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A, B, C))))))),
% 0.20/0.59 inference(skolemize,[status(sab)],[59])).
% 0.20/0.59 tff(61,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.59 tff(62,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.20/0.59 tff(63,plain,
% 0.20/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(64,plain,
% 0.20/0.59 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (v3_struct_0(A!0) | (~m1_subset_1(C, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(65,plain,
% 0.20/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (v3_struct_0(A!0) | (~m1_subset_1(C, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.59 tff(66,plain,
% 0.20/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (v3_struct_0(A!0) | (~m1_subset_1(C, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.59 tff(67,plain,
% 0.20/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : (v3_struct_0(A!0) | (~m1_subset_1(C, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(68,plain,
% 0.20/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, k22_filter_2(A, B, C))) | (~v10_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v15_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~v16_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))) | (~l3_lattices(k23_filter_2(A, k22_filter_2(A, B, C)))))) | (~v15_lattices(A)) | (~v16_lattices(A)) | (~v12_lattices(A)) | (~r3_lattices(A, B, C)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.60 tff(69,plain,
% 0.20/0.60 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[68, 35, 34, 33, 62])).
% 0.20/0.60 tff(70,plain,
% 0.20/0.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C))))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(71,plain,
% 0.20/0.60 (((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C))))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(72,plain,
% 0.20/0.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))))),
% 0.20/0.60 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.60 tff(73,plain,
% 0.20/0.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C))))),
% 0.20/0.60 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.60 tff(74,plain,
% 0.20/0.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C))))),
% 0.20/0.60 inference(quant_inst,[status(thm)],[])).
% 0.20/0.60 tff(75,plain,
% 0.20/0.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B, C)))))) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B, C))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.60 tff(76,plain,
% 0.20/0.60 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[75, 32, 69])).
% 0.20/0.60 tff(77,plain,
% 0.20/0.60 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(78,plain,
% 0.20/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.60 tff(79,plain,
% 0.20/0.60 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) <=> (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v17_lattices(A)) <=> (~(v3_struct_0(A) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v17_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v17_lattices(A))) <=> (v3_struct_0(A) | (~v17_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (v3_struct_0(A) | (~v17_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (v3_struct_0(A) | (~v17_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(80,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.60 tff(81,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(82,plain,
% 0.20/0.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A)) & v14_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A)))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A)) & v15_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A)))), (((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))), (((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A))) <=> (((~v3_struct_0(A)) & v17_lattices(A)) => ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))))), rewrite((((~v3_struct_0(A)) & v17_lattices(A)) => ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))) <=> ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A))) <=> ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(83,plain,
% 0.20/0.60 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.60 tff(84,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc5_lattices')).
% 0.20/0.60 tff(85,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.60 tff(86,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.20/0.60 tff(87,plain,(
% 0.20/0.60 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.20/0.60 inference(skolemize,[status(sab)],[86])).
% 0.20/0.60 tff(88,plain,
% 0.20/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.60 tff(89,plain,
% 0.20/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.20/0.60 tff(90,plain,
% 0.20/0.60 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & r3_lattices(A!0, B!1, C!2)),
% 0.20/0.60 inference(or_elim,[status(thm)],[30])).
% 0.20/0.60 tff(91,plain,
% 0.20/0.60 (v17_lattices(A!0)),
% 0.20/0.60 inference(and_elim,[status(thm)],[90])).
% 0.20/0.60 tff(92,plain,
% 0.20/0.60 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0)))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(93,plain,
% 0.20/0.60 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0)))),
% 0.20/0.60 inference(quant_inst,[status(thm)],[])).
% 0.20/0.60 tff(94,plain,
% 0.20/0.60 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.60 tff(95,plain,
% 0.20/0.60 (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[94, 35, 33, 91, 89])).
% 0.20/0.60 tff(96,plain,
% 0.20/0.60 ((v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v16_lattices(A!0)),
% 0.20/0.60 inference(tautology,[status(thm)],[])).
% 0.20/0.60 tff(97,plain,
% 0.20/0.60 (v16_lattices(A!0)),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.60 tff(98,plain,
% 0.20/0.60 ((v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v15_lattices(A!0)),
% 0.20/0.60 inference(tautology,[status(thm)],[])).
% 0.20/0.60 tff(99,plain,
% 0.20/0.60 (v15_lattices(A!0)),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.20/0.60 tff(100,plain,
% 0.20/0.60 ((v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v11_lattices(A!0)),
% 0.20/0.60 inference(tautology,[status(thm)],[])).
% 0.20/0.60 tff(101,plain,
% 0.20/0.60 (v11_lattices(A!0)),
% 0.20/0.60 inference(unit_resolution,[status(thm)],[100, 95])).
% 0.20/0.60 tff(102,plain,
% 0.20/0.60 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A))))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(103,plain,
% 0.20/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.60 tff(104,plain,
% 0.20/0.60 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(105,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.60 tff(106,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))),
% 0.20/0.60 inference(rewrite,[status(thm)],[])).
% 0.20/0.60 tff(107,plain,
% 0.20/0.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) & v10_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) & v10_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A))), (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A)))), ((((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A)) & v12_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A)) & v12_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A))), ((((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) => (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) => (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A))))), ((l3_lattices(A) => ((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) => (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))), ((l3_lattices(A) => ((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) => (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))))),
% 0.20/0.60 inference(bind,[status(th)],[])).
% 0.20/0.60 tff(108,plain,
% 0.20/0.60 (![A: $i] : (l3_lattices(A) => ((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) => (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))),
% 0.20/0.60 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.60 tff(109,axiom,(![A: $i] : (l3_lattices(A) => ((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) => (((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & v10_lattices(A)) & v12_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc7_lattices')).
% 0.20/0.60 tff(110,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.60 tff(111,plain,
% 0.20/0.60 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.20/0.60 tff(112,plain,(
% 0.20/0.60 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))))),
% 0.20/0.60 inference(skolemize,[status(sab)],[111])).
% 0.20/0.60 tff(113,plain,
% 0.20/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))),
% 0.20/0.60 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.60 tff(114,plain,
% 0.20/0.61 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))),
% 0.20/0.61 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.20/0.61 tff(115,plain,
% 0.20/0.61 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 0.20/0.61 inference(rewrite,[status(thm)],[])).
% 0.20/0.61 tff(116,plain,
% 0.20/0.61 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~v10_lattices(A!0)) | (~v12_lattices(A!0))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 0.20/0.61 inference(rewrite,[status(thm)],[])).
% 0.20/0.61 tff(117,plain,
% 0.20/0.61 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 0.20/0.61 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.61 tff(118,plain,
% 0.20/0.61 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[117, 115])).
% 0.57/0.61 tff(119,plain,
% 0.57/0.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)))))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(120,plain,
% 0.57/0.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~v10_lattices(A)) | (~v12_lattices(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.57/0.61 tff(121,plain,
% 0.57/0.61 ((~v11_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[120, 35, 34, 33, 114])).
% 0.57/0.61 tff(122,plain,
% 0.57/0.61 (~(v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[121, 101])).
% 0.57/0.61 tff(123,plain,
% 0.57/0.61 ((v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~v12_lattices(A!0)) | (~v7_lattices(A!0)) | (~v6_lattices(A!0)) | (~v5_lattices(A!0)) | (~v4_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v12_lattices(A!0)),
% 0.57/0.61 inference(tautology,[status(thm)],[])).
% 0.57/0.61 tff(124,plain,
% 0.57/0.61 (v12_lattices(A!0)),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.57/0.61 tff(125,plain,
% 0.57/0.61 (r3_lattices(A!0, B!1, C!2)),
% 0.57/0.61 inference(and_elim,[status(thm)],[90])).
% 0.57/0.61 tff(126,plain,
% 0.57/0.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(127,plain,
% 0.57/0.61 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(128,plain,
% 0.57/0.61 ((~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) <=> (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(129,plain,
% 0.57/0.61 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)))),
% 0.57/0.61 inference(monotonicity,[status(thm)],[128])).
% 0.57/0.61 tff(130,plain,
% 0.57/0.61 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[129, 127])).
% 0.57/0.61 tff(131,plain,
% 0.57/0.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))))),
% 0.57/0.61 inference(monotonicity,[status(thm)],[130])).
% 0.57/0.61 tff(132,plain,
% 0.57/0.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[131, 126])).
% 0.57/0.61 tff(133,plain,
% 0.57/0.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))) | (~r3_lattices(A!0, B!1, C!2)))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(134,plain,
% 0.57/0.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C)))))) | (~r3_lattices(A!0, B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~v12_lattices(A!0)) | (~r3_lattices(A!0, B!1, C!2)) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.57/0.61 tff(135,plain,
% 0.57/0.61 (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[134, 35, 34, 33, 125, 31, 124, 99, 97, 76])).
% 0.57/0.62 tff(136,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) | (~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(137,plain,
% 0.57/0.62 (~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.57/0.62 tff(138,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) | v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(139,plain,
% 0.57/0.62 (v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.57/0.62 tff(140,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) | l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(141,plain,
% 0.57/0.62 (l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[140, 135])).
% 0.57/0.62 tff(142,plain,
% 0.57/0.62 ((~(~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))) <=> (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(143,plain,
% 0.57/0.62 (((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) <=> (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(144,plain,
% 0.57/0.62 ((~((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) <=> (~(~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[143])).
% 0.57/0.62 tff(145,plain,
% 0.57/0.62 ((~((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) <=> (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))),
% 0.57/0.62 inference(transitivity,[status(thm)],[144, 142])).
% 0.57/0.62 tff(146,plain,
% 0.57/0.62 (~((~v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) & v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) & l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))),
% 0.57/0.62 inference(or_elim,[status(thm)],[30])).
% 0.57/0.62 tff(147,plain,
% 0.57/0.62 (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.57/0.62 tff(148,plain,
% 0.57/0.62 (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[147, 141, 139, 137])).
% 0.57/0.62 tff(149,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) | v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(150,plain,
% 0.57/0.62 (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.57/0.62 tff(151,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) | v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(152,plain,
% 0.57/0.62 (v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[151, 135])).
% 0.57/0.62 tff(153,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v10_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))) | v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(154,plain,
% 0.57/0.62 (v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[153, 135])).
% 0.57/0.62 tff(155,plain,
% 0.57/0.62 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(156,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[155])).
% 0.57/0.62 tff(157,plain,
% 0.57/0.62 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v17_lattices(A)) <=> (~(v3_struct_0(A) | (~v17_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)) <=> (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))) <=> (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))), ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) <=> (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), ((((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ((~(v3_struct_0(A) | (~v17_lattices(A)))) | (~l3_lattices(A)) | (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))))), rewrite(((~(v3_struct_0(A) | (~v17_lattices(A)))) | (~l3_lattices(A)) | (v3_struct_0(A) | (~v11_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))), ((((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(158,plain,
% 0.57/0.62 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[157])).
% 0.57/0.62 tff(159,plain,
% 0.57/0.62 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(160,plain,
% 0.57/0.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))) <=> ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A)))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))) <=> ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A))))), ((l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))) | ((~v3_struct_0(A)) & v17_lattices(A)))) <=> (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))), ((l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A)))) <=> (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(161,plain,
% 0.57/0.62 (![A: $i] : (l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[160])).
% 0.57/0.62 tff(162,axiom,(![A: $i] : (l3_lattices(A) => (((((~v3_struct_0(A)) & v11_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) => ((~v3_struct_0(A)) & v17_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc6_lattices')).
% 0.57/0.62 tff(163,plain,
% 0.57/0.62 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.57/0.62 tff(164,plain,
% 0.57/0.62 (![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.57/0.62 tff(165,plain,(
% 0.57/0.62 ![A: $i] : (((~v3_struct_0(A)) & v17_lattices(A)) | (~l3_lattices(A)) | (~((~v3_struct_0(A)) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A))))),
% 0.57/0.62 inference(skolemize,[status(sab)],[164])).
% 0.57/0.62 tff(166,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.57/0.62 tff(167,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[166, 156])).
% 0.57/0.62 tff(168,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(169,plain,
% 0.57/0.62 ((v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))) <=> (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(170,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[169])).
% 0.57/0.62 tff(171,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.62 inference(transitivity,[status(thm)],[170, 168])).
% 0.57/0.62 tff(172,plain,
% 0.57/0.62 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | (v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))))))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(173,plain,
% 0.57/0.62 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v15_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~(v3_struct_0(A) | (~v17_lattices(A)))))) | v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~l3_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v15_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v16_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))) | (~(v3_struct_0(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v17_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.57/0.62 tff(174,plain,
% 0.57/0.62 (~v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[173, 137, 141, 167, 154, 152, 150])).
% 0.57/0.62 tff(175,plain,
% 0.57/0.62 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(176,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[175])).
% 0.57/0.62 tff(177,plain,
% 0.57/0.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(178,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[177])).
% 0.57/0.62 tff(179,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))),
% 0.57/0.62 inference(transitivity,[status(thm)],[178, 176])).
% 0.57/0.62 tff(180,plain,
% 0.57/0.62 (^[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)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), rewrite((~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A))))), ((v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (v1_xboole_0(B) | (~m2_lattice4(B, A)))))), rewrite((v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (v1_xboole_0(B) | (~m2_lattice4(B, A)))) <=> (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))), ((v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))))), (![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(181,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[180])).
% 0.57/0.62 tff(182,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(183,plain,
% 0.57/0.62 (^[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(rewrite((v11_lattices(A) => v11_lattices(k23_filter_2(A, B))) <=> ((~v11_lattices(A)) | v11_lattices(k23_filter_2(A, B)))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B)))) <=> (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ((~v11_lattices(A)) | v11_lattices(k23_filter_2(A, B)))))), rewrite((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ((~v11_lattices(A)) | v11_lattices(k23_filter_2(A, B)))) <=> (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B)))) <=> (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))))), (![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B)))) <=> ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(184,plain,
% 0.57/0.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[183])).
% 0.57/0.63 tff(185,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v11_lattices(A) => v11_lattices(k23_filter_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t78_filter_2')).
% 0.57/0.63 tff(186,plain,
% 0.57/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.57/0.63 tff(187,plain,
% 0.57/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.57/0.63 tff(188,plain,(
% 0.57/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v11_lattices(k23_filter_2(A, B)) | (~v11_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 0.57/0.63 inference(skolemize,[status(sab)],[187])).
% 0.57/0.63 tff(189,plain,
% 0.57/0.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.57/0.63 tff(190,plain,
% 0.57/0.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[189, 179])).
% 0.57/0.63 tff(191,plain,
% 0.57/0.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0))))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(192,plain,
% 0.57/0.63 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A!0, B)) | (~m2_lattice4(B, A!0)) | (~v11_lattices(A!0)))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0))))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(193,plain,
% 0.57/0.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A!0, B)) | (~m2_lattice4(B, A!0)) | (~v11_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[192])).
% 0.59/0.63 tff(194,plain,
% 0.59/0.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A!0, B)) | (~m2_lattice4(B, A!0)) | (~v11_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0))))),
% 0.59/0.63 inference(transitivity,[status(thm)],[193, 191])).
% 0.59/0.63 tff(195,plain,
% 0.59/0.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A!0, B)) | (~m2_lattice4(B, A!0)) | (~v11_lattices(A!0))))),
% 0.59/0.63 inference(quant_inst,[status(thm)],[])).
% 0.59/0.63 tff(196,plain,
% 0.59/0.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | v11_lattices(k23_filter_2(A, B)) | (~m2_lattice4(B, A)) | (~v11_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))),
% 0.59/0.63 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.59/0.63 tff(197,plain,
% 0.59/0.63 (![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))),
% 0.59/0.63 inference(unit_resolution,[status(thm)],[196, 35, 34, 33, 190])).
% 0.59/0.63 tff(198,plain,
% 0.59/0.63 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | ((~v11_lattices(A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | (~v11_lattices(A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(199,plain,
% 0.59/0.63 ((v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v11_lattices(A!0))) <=> ((~v11_lattices(A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(200,plain,
% 0.59/0.63 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | (v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v11_lattices(A!0)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | ((~v11_lattices(A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[199])).
% 0.59/0.63 tff(201,plain,
% 0.59/0.63 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | (v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v11_lattices(A!0)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | (~v11_lattices(A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)))),
% 0.60/0.63 inference(transitivity,[status(thm)],[200, 198])).
% 0.60/0.63 tff(202,plain,
% 0.60/0.63 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | (v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | (~v11_lattices(A!0)))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(203,plain,
% 0.60/0.63 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | v11_lattices(k23_filter_2(A!0, B)) | (~v11_lattices(A!0)))) | (~v11_lattices(A!0)) | v11_lattices(k23_filter_2(A!0, k22_filter_2(A!0, B!1, C!2))) | v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.60/0.63 tff(204,plain,
% 0.60/0.63 (v1_xboole_0(k22_filter_2(A!0, B!1, C!2)) | (~m2_lattice4(k22_filter_2(A!0, B!1, C!2), A!0))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[203, 197, 101, 174])).
% 0.60/0.63 tff(205,plain,
% 0.60/0.63 ($false),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[204, 46, 44])).
% 0.60/0.63 % SZS output end Proof
%------------------------------------------------------------------------------