TSTP Solution File: LAT310+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT310+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 18:32:57 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
% 0.11/0.11 % Problem : LAT310+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 13:22:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.58 % SZS status Theorem
% 0.20/0.58 % SZS output start Proof
% 0.20/0.58 tff(r1_tarski_type, type, (
% 0.20/0.58 r1_tarski: ( $i * $i ) > $o)).
% 0.20/0.58 tff(k19_filter_2_type, type, (
% 0.20/0.58 k19_filter_2: ( $i * $i ) > $i)).
% 0.20/0.58 tff(tptp_fun_D_3_type, type, (
% 0.20/0.58 tptp_fun_D_3: $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_filter_2_type, type, (
% 0.20/0.58 m2_filter_2: ( $i * $i ) > $o)).
% 0.20/0.58 tff(tptp_fun_D_4_type, type, (
% 0.20/0.58 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 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(k1_zfmisc_1_type, type, (
% 0.20/0.58 k1_zfmisc_1: $i > $i)).
% 0.20/0.58 tff(u1_struct_0_type, type, (
% 0.20/0.58 u1_struct_0: $i > $i)).
% 0.20/0.58 tff(m2_lattice4_type, type, (
% 0.20/0.58 m2_lattice4: ( $i * $i ) > $o)).
% 0.20/0.58 tff(v1_xboole_0_type, type, (
% 0.20/0.58 v1_xboole_0: $i > $o)).
% 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(tptp_fun_B_1_type, type, (
% 0.20/0.58 tptp_fun_B_1: $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(1,plain,
% 0.20/0.58 (^[A: $i, B: $i] : refl((v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(2,plain,
% 0.20/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(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] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> ((v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k19_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k19_filter_2(A, B), A)) <=> (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(4,plain,
% 0.20/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(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] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(6,plain,
% 0.20/0.58 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m2_filter_2(k19_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m2_filter_2(k19_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m2_filter_2(k19_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m2_filter_2(k19_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A))))),
% 0.20/0.58 inference(bind,[status(th)],[])).
% 0.20/0.58 tff(7,plain,
% 0.20/0.58 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m2_filter_2(k19_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.58 tff(8,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m2_filter_2(k19_filter_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k19_filter_2')).
% 0.20/0.58 tff(9,plain,
% 0.20/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), 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] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), 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] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m2_filter_2(k19_filter_2(A, B), 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] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(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] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(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)) & ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(15,plain,
% 0.20/0.58 ((((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) & ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))) <=> ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(16,plain,
% 0.20/0.58 ((((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))) <=> ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(17,plain,
% 0.20/0.58 ((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(18,plain,
% 0.20/0.58 (((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))) <=> (((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.58 tff(19,plain,
% 0.20/0.58 (((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))) <=> ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[18, 16])).
% 0.20/0.58 tff(20,plain,
% 0.20/0.58 ((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(21,plain,
% 0.20/0.58 (((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) & ((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))) <=> (((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) & ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[20, 19])).
% 0.20/0.58 tff(22,plain,
% 0.20/0.58 (((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) & ((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))) <=> ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[21, 15])).
% 0.20/0.58 tff(23,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(24,plain,
% 0.20/0.58 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) & ((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[23, 22])).
% 0.20/0.58 tff(25,plain,
% 0.20/0.58 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~((~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) & ((~(~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[24, 14])).
% 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] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B))))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 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] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => ((r1_tarski(C, D) => r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B))))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(28,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A)))) => ((r1_tarski(C, D) => r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t39_filter_2')).
% 0.20/0.58 tff(29,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.58 tff(30,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.20/0.58 tff(31,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.20/0.58 tff(32,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.58 tff(33,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.20/0.58 tff(34,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.58 tff(35,plain,
% 0.20/0.58 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(A))))) | (((~r1_tarski(C, D)) | r1_tarski(k19_filter_2(A, C), k19_filter_2(A, D))) & r1_tarski(k19_filter_2(A, k19_filter_2(A, B)), k19_filter_2(A, B)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.20/0.58 tff(36,plain,
% 0.20/0.58 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~v1_xboole_0(B!1)) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))) & (~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) & (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.20/0.59 tff(37,plain,
% 0.20/0.59 (~((~((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0))))) | (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))),
% 0.20/0.59 inference(and_elim,[status(thm)],[36])).
% 0.20/0.59 tff(38,plain,
% 0.20/0.59 ((~v1_xboole_0(D!3)) & m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.59 inference(or_elim,[status(thm)],[37])).
% 0.20/0.59 tff(39,plain,
% 0.20/0.59 (m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.20/0.59 inference(and_elim,[status(thm)],[38])).
% 0.20/0.59 tff(40,plain,
% 0.20/0.59 (~v1_xboole_0(D!3)),
% 0.20/0.59 inference(and_elim,[status(thm)],[38])).
% 0.20/0.59 tff(41,plain,
% 0.20/0.59 (l3_lattices(A!0)),
% 0.20/0.59 inference(and_elim,[status(thm)],[36])).
% 0.20/0.59 tff(42,plain,
% 0.20/0.59 (v10_lattices(A!0)),
% 0.20/0.59 inference(and_elim,[status(thm)],[36])).
% 0.20/0.59 tff(43,plain,
% 0.20/0.59 (~v3_struct_0(A!0)),
% 0.20/0.59 inference(and_elim,[status(thm)],[36])).
% 0.20/0.59 tff(44,plain,
% 0.20/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(D!3) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, D!3), A!0))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | v1_xboole_0(D!3) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, D!3), A!0))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(45,plain,
% 0.20/0.59 ((v3_struct_0(A!0) | v1_xboole_0(D!3) | m2_filter_2(k19_filter_2(A!0, D!3), A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | v1_xboole_0(D!3) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, D!3), A!0))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(46,plain,
% 0.20/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(D!3) | m2_filter_2(k19_filter_2(A!0, D!3), A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(D!3) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, D!3), A!0)))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.59 tff(47,plain,
% 0.20/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(D!3) | m2_filter_2(k19_filter_2(A!0, D!3), A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | v1_xboole_0(D!3) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, D!3), A!0))),
% 0.20/0.59 inference(transitivity,[status(thm)],[46, 44])).
% 0.20/0.59 tff(48,plain,
% 0.20/0.59 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(D!3) | m2_filter_2(k19_filter_2(A!0, D!3), A!0) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(49,plain,
% 0.20/0.59 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | v1_xboole_0(D!3) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, D!3), A!0)),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.59 tff(50,plain,
% 0.20/0.59 (m2_filter_2(k19_filter_2(A!0, D!3), A!0)),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[49, 43, 42, 41, 40, 39, 13])).
% 0.20/0.59 tff(51,plain,
% 0.20/0.59 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(52,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.59 tff(53,plain,
% 0.20/0.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(54,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.59 tff(55,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.59 tff(56,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(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(57,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[56])).
% 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] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(59,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] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 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] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.59 tff(61,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.20/0.59 tff(62,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.59 tff(63,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.59 tff(64,plain,(
% 0.20/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.20/0.59 inference(skolemize,[status(sab)],[63])).
% 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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[64, 57])).
% 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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[65, 55])).
% 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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.20/0.59 inference(rewrite,[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] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(69,plain,
% 0.20/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.59 tff(70,plain,
% 0.20/0.59 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[69, 43, 42, 41, 66])).
% 0.20/0.59 tff(71,plain,
% 0.20/0.59 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0)))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(72,plain,
% 0.20/0.59 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(73,plain,
% 0.20/0.59 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.59 tff(74,plain,
% 0.20/0.59 (~(v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[73, 70, 50])).
% 0.20/0.59 tff(75,plain,
% 0.20/0.59 ((v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0))) | m2_lattice4(k19_filter_2(A!0, D!3), A!0)),
% 0.20/0.59 inference(tautology,[status(thm)],[])).
% 0.20/0.59 tff(76,plain,
% 0.20/0.59 (m2_lattice4(k19_filter_2(A!0, D!3), A!0)),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.59 tff(77,plain,
% 0.20/0.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(78,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.59 tff(79,plain,
% 0.20/0.59 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(80,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.59 tff(81,plain,
% 0.20/0.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(82,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.59 tff(83,plain,
% 0.20/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.59 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.59 tff(84,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))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(85,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.59 tff(86,plain,
% 0.20/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(87,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] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.57/0.59 inference(bind,[status(th)],[])).
% 0.57/0.59 tff(88,plain,
% 0.57/0.59 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.57/0.59 inference(quant_intro,[status(thm)],[87])).
% 0.57/0.59 tff(89,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.57/0.59 tff(90,plain,
% 0.57/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.57/0.59 tff(91,plain,
% 0.57/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.57/0.59 tff(92,plain,(
% 0.57/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.57/0.59 inference(skolemize,[status(sab)],[91])).
% 0.57/0.59 tff(93,plain,
% 0.57/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.57/0.59 tff(94,plain,
% 0.57/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.57/0.59 tff(95,plain,
% 0.57/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[94, 78])).
% 0.57/0.59 tff(96,plain,
% 0.57/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(97,plain,
% 0.57/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.57/0.59 inference(quant_inst,[status(thm)],[])).
% 0.57/0.59 tff(98,plain,
% 0.57/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.57/0.59 tff(99,plain,
% 0.57/0.59 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[98, 43, 42, 41, 95])).
% 0.57/0.59 tff(100,plain,
% 0.57/0.59 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k19_filter_2(A!0, D!3), A!0)) | m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0)) | m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(101,plain,
% 0.57/0.59 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k19_filter_2(A!0, D!3), A!0)) | m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.57/0.59 inference(quant_inst,[status(thm)],[])).
% 0.57/0.59 tff(102,plain,
% 0.57/0.59 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0)) | m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.57/0.59 tff(103,plain,
% 0.57/0.59 (m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[102, 99, 76])).
% 0.57/0.59 tff(104,plain,
% 0.57/0.59 ((v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m2_lattice4(k19_filter_2(A!0, D!3), A!0))) | (~v1_xboole_0(k19_filter_2(A!0, D!3)))),
% 0.57/0.59 inference(tautology,[status(thm)],[])).
% 0.57/0.59 tff(105,plain,
% 0.57/0.59 (~v1_xboole_0(k19_filter_2(A!0, D!3))),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[104, 74])).
% 0.57/0.59 tff(106,plain,
% 0.57/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(107,plain,
% 0.57/0.59 ((v3_struct_0(A!0) | v1_xboole_0(k19_filter_2(A!0, D!3)) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(108,plain,
% 0.57/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(k19_filter_2(A!0, D!3)) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)))),
% 0.57/0.60 inference(monotonicity,[status(thm)],[107])).
% 0.57/0.60 tff(109,plain,
% 0.57/0.60 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(k19_filter_2(A!0, D!3)) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0))),
% 0.57/0.60 inference(transitivity,[status(thm)],[108, 106])).
% 0.57/0.60 tff(110,plain,
% 0.57/0.60 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(k19_filter_2(A!0, D!3)) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.57/0.60 inference(quant_inst,[status(thm)],[])).
% 0.57/0.60 tff(111,plain,
% 0.57/0.60 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.57/0.60 tff(112,plain,
% 0.57/0.60 (m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[111, 43, 42, 41, 13, 105, 103])).
% 0.57/0.60 tff(113,plain,
% 0.57/0.60 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(114,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[113])).
% 0.57/0.60 tff(115,plain,
% 0.57/0.60 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(116,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[115])).
% 0.57/0.60 tff(117,plain,
% 0.57/0.60 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(118,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[117])).
% 0.57/0.60 tff(119,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 0.57/0.60 inference(transitivity,[status(thm)],[118, 116])).
% 0.57/0.60 tff(120,plain,
% 0.57/0.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))) <=> ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))), (![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))) <=> ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(121,plain,
% 0.57/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[120])).
% 0.57/0.60 tff(122,plain,
% 0.57/0.60 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | ((~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(123,plain,
% 0.57/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | ((~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[122])).
% 0.57/0.60 tff(124,plain,
% 0.57/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(125,plain,
% 0.57/0.60 (^[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(rewrite(((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D))))) <=> ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))), ((m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D)))))) <=> (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))), rewrite((m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))) <=> ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))), ((m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D)))))) <=> ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))), (![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D)))))) <=> ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D))))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(126,plain,
% 0.57/0.60 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[125])).
% 0.57/0.60 tff(127,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (m2_filter_2(C, A) => ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (m2_filter_2(D, A) => (r1_tarski(B, D) => r1_tarski(C, D))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d11_filter_2')).
% 0.57/0.60 tff(128,plain,
% 0.57/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.57/0.60 tff(129,plain,
% 0.57/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | ((C = k19_filter_2(A, B)) <=> (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.57/0.60 tff(130,plain,(
% 0.57/0.60 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | ((~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A))))))))))),
% 0.57/0.60 inference(skolemize,[status(sab)],[129])).
% 0.57/0.60 tff(131,plain,
% 0.57/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~m2_filter_2(C, A)) | (((~(C = k19_filter_2(A, B))) | (r1_tarski(B, C) & ![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A))))) & ((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.57/0.60 tff(132,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.57/0.60 tff(133,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))) | (~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[132, 119])).
% 0.57/0.60 tff(134,plain,
% 0.57/0.60 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[133, 114])).
% 0.57/0.60 tff(135,plain,
% 0.57/0.60 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(136,plain,
% 0.57/0.60 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((C = k19_filter_2(A!0, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(137,plain,
% 0.57/0.60 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((C = k19_filter_2(A!0, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))))),
% 0.57/0.60 inference(monotonicity,[status(thm)],[136])).
% 0.57/0.60 tff(138,plain,
% 0.57/0.60 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((C = k19_filter_2(A!0, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[137, 135])).
% 0.57/0.61 tff(139,plain,
% 0.57/0.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((C = k19_filter_2(A!0, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0)))))))))))))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(140,plain,
% 0.57/0.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : ((~m2_filter_2(C, A)) | (~((~((C = k19_filter_2(A, B)) | (~r1_tarski(B, C)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A))) | (~m2_filter_2(tptp_fun_D_4(C, B, A), A)))))) | (~((~(C = k19_filter_2(A, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A)))))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.57/0.61 tff(141,plain,
% 0.57/0.61 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[140, 43, 42, 41, 134])).
% 0.57/0.61 tff(142,plain,
% 0.57/0.61 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D))))))))))))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(143,plain,
% 0.58/0.61 ((v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(D!3, D)) | (~m2_filter_2(D, A!0)))))))))))) <=> (v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D))))))))))))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(144,plain,
% 0.58/0.61 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(D!3, D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[143])).
% 0.58/0.61 tff(145,plain,
% 0.58/0.61 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(D!3, D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D))))))))))))),
% 0.58/0.61 inference(transitivity,[status(thm)],[144, 142])).
% 0.58/0.61 tff(146,plain,
% 0.58/0.61 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(D!3, D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.58/0.61 inference(quant_inst,[status(thm)],[])).
% 0.58/0.61 tff(147,plain,
% 0.58/0.61 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(D!3) | (~m1_subset_1(D!3, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))),
% 0.58/0.61 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.58/0.61 tff(148,plain,
% 0.58/0.61 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))),
% 0.58/0.61 inference(unit_resolution,[status(thm)],[147, 40, 39, 141])).
% 0.58/0.61 tff(149,plain,
% 0.58/0.61 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))))))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(150,plain,
% 0.58/0.61 (((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D))))))))))) <=> ((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))))))),
% 0.58/0.61 inference(rewrite,[status(thm)],[])).
% 0.58/0.61 tff(151,plain,
% 0.58/0.61 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))))))))))),
% 0.58/0.61 inference(monotonicity,[status(thm)],[150])).
% 0.58/0.61 tff(152,plain,
% 0.58/0.61 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))))))),
% 0.58/0.62 inference(transitivity,[status(thm)],[151, 149])).
% 0.58/0.62 tff(153,plain,
% 0.58/0.62 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))),
% 0.58/0.62 inference(quant_inst,[status(thm)],[])).
% 0.58/0.62 tff(154,plain,
% 0.58/0.62 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))))))))),
% 0.58/0.62 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.58/0.62 tff(155,plain,
% 0.58/0.62 (~((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[154, 148, 112])).
% 0.58/0.62 tff(156,plain,
% 0.58/0.62 (((~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))))))) | ((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))),
% 0.58/0.62 inference(tautology,[status(thm)],[])).
% 0.58/0.62 tff(157,plain,
% 0.58/0.62 ((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))))),
% 0.58/0.62 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.58/0.62 tff(158,plain,
% 0.58/0.62 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D))))))))))))),
% 0.58/0.62 inference(rewrite,[status(thm)],[])).
% 0.58/0.62 tff(159,plain,
% 0.58/0.62 ((v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, D!3), D)) | (~m2_filter_2(D, A!0)))))))))))) <=> (v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D))))))))))))),
% 0.60/0.62 inference(rewrite,[status(thm)],[])).
% 0.60/0.62 tff(160,plain,
% 0.60/0.62 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, D!3), D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))))),
% 0.60/0.62 inference(monotonicity,[status(thm)],[159])).
% 0.60/0.62 tff(161,plain,
% 0.60/0.62 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, D!3), D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D))))))))))))),
% 0.60/0.62 inference(transitivity,[status(thm)],[160, 158])).
% 0.60/0.62 tff(162,plain,
% 0.60/0.62 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, D!3), D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.60/0.62 inference(quant_inst,[status(thm)],[])).
% 0.60/0.62 tff(163,plain,
% 0.60/0.62 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(k19_filter_2(A!0, D!3)) | (~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))),
% 0.60/0.62 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.60/0.62 tff(164,plain,
% 0.60/0.62 ((~m1_subset_1(k19_filter_2(A!0, D!3), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[163, 141, 105])).
% 0.60/0.63 tff(165,plain,
% 0.60/0.63 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[164, 103])).
% 0.60/0.63 tff(166,plain,
% 0.60/0.63 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(167,plain,
% 0.60/0.63 (((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D))))))))))) <=> ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(168,plain,
% 0.60/0.63 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))))))))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[167])).
% 0.60/0.63 tff(169,plain,
% 0.60/0.63 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))))))),
% 0.60/0.63 inference(transitivity,[status(thm)],[168, 166])).
% 0.60/0.63 tff(170,plain,
% 0.60/0.63 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(171,plain,
% 0.60/0.63 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, D!3), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~((~r1_tarski(k19_filter_2(A!0, D!3), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, D!3), D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.60/0.63 tff(172,plain,
% 0.60/0.63 (~((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[171, 50, 165])).
% 0.60/0.63 tff(173,plain,
% 0.60/0.63 (((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))))) | ((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))),
% 0.60/0.63 inference(tautology,[status(thm)],[])).
% 0.60/0.63 tff(174,plain,
% 0.60/0.63 ((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.60/0.63 tff(175,plain,
% 0.60/0.63 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(176,plain,
% 0.60/0.63 (((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D))))))))))) <=> ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(177,plain,
% 0.60/0.63 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D)))))))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[176])).
% 0.60/0.63 tff(178,plain,
% 0.60/0.63 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))))))),
% 0.60/0.64 inference(transitivity,[status(thm)],[177, 175])).
% 0.60/0.64 tff(179,plain,
% 0.60/0.64 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3)) | (~(r1_tarski(k19_filter_2(A!0, D!3), tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, D!3), D!3, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, D!3) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, D!3), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(180,plain,
% 0.60/0.64 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(D!3, C)) | (C = k19_filter_2(A!0, D!3)) | (~(r1_tarski(C, tptp_fun_D_4(C, D!3, A!0)) | (~r1_tarski(D!3, tptp_fun_D_4(C, D!3, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, D!3, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D)))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.60/0.64 tff(181,plain,
% 0.60/0.64 (~((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[180, 50, 148])).
% 0.60/0.64 tff(182,plain,
% 0.60/0.64 (((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D)))) | ![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(183,plain,
% 0.60/0.64 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.60/0.64 tff(184,plain,
% 0.60/0.64 (((~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D)))) | r1_tarski(D!3, k19_filter_2(A!0, D!3))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(185,plain,
% 0.60/0.64 (r1_tarski(D!3, k19_filter_2(A!0, D!3))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[184, 181])).
% 0.60/0.64 tff(186,plain,
% 0.60/0.64 (((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))) <=> ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(187,plain,
% 0.60/0.64 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))) | ((~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(188,plain,
% 0.60/0.64 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, D!3), D))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(D!3, k19_filter_2(A!0, D!3))) | r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.60/0.64 tff(189,plain,
% 0.60/0.64 (r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[188, 50, 185, 183])).
% 0.60/0.64 tff(190,plain,
% 0.60/0.64 ((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(191,plain,
% 0.60/0.64 ((~((~r1_tarski(k19_filter_2(A!0, D!3), k19_filter_2(A!0, D!3))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))))) | (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.60/0.64 tff(192,plain,
% 0.60/0.64 (k19_filter_2(A!0, D!3) = k19_filter_2(A!0, k19_filter_2(A!0, D!3))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[191, 174])).
% 0.60/0.64 tff(193,plain,
% 0.60/0.64 (k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3)),
% 0.60/0.64 inference(symmetry,[status(thm)],[192])).
% 0.60/0.64 tff(194,plain,
% 0.60/0.64 ((~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))) | (~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(195,plain,
% 0.60/0.64 ((~((~(k19_filter_2(A!0, k19_filter_2(A!0, D!3)) = k19_filter_2(A!0, D!3))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))))) | (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.60/0.64 tff(196,plain,
% 0.60/0.64 (~((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[195, 157])).
% 0.60/0.64 tff(197,plain,
% 0.60/0.64 (((~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(D!3, D)) | r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, D!3)), D)))) | r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(198,plain,
% 0.60/0.64 (r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.60/0.64 tff(199,plain,
% 0.60/0.64 (r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) <=> r1_tarski(C!2, k19_filter_2(A!0, D!3))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[193])).
% 0.60/0.64 tff(200,plain,
% 0.60/0.64 (r1_tarski(C!2, k19_filter_2(A!0, D!3)) <=> r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.64 inference(symmetry,[status(thm)],[199])).
% 0.60/0.64 tff(201,plain,
% 0.60/0.64 ((~r1_tarski(C!2, k19_filter_2(A!0, D!3))) <=> (~r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[200])).
% 0.60/0.64 tff(202,plain,
% 0.60/0.64 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.64 inference(and_elim,[status(thm)],[36])).
% 0.60/0.64 tff(203,plain,
% 0.60/0.64 (~v1_xboole_0(B!1)),
% 0.60/0.64 inference(and_elim,[status(thm)],[36])).
% 0.60/0.64 tff(204,plain,
% 0.60/0.64 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, B!1), A!0))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, B!1), A!0))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(205,plain,
% 0.60/0.64 ((v3_struct_0(A!0) | v1_xboole_0(B!1) | m2_filter_2(k19_filter_2(A!0, B!1), A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, B!1), A!0))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(206,plain,
% 0.60/0.64 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | m2_filter_2(k19_filter_2(A!0, B!1), A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, B!1), A!0)))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[205])).
% 0.60/0.64 tff(207,plain,
% 0.60/0.64 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | m2_filter_2(k19_filter_2(A!0, B!1), A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, B!1), A!0))),
% 0.60/0.64 inference(transitivity,[status(thm)],[206, 204])).
% 0.60/0.64 tff(208,plain,
% 0.60/0.64 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | m2_filter_2(k19_filter_2(A!0, B!1), A!0) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(209,plain,
% 0.60/0.64 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(B!1) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, B!1), A!0)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.60/0.64 tff(210,plain,
% 0.60/0.64 (m2_filter_2(k19_filter_2(A!0, B!1), A!0)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[209, 43, 42, 41, 203, 202, 13])).
% 0.60/0.64 tff(211,plain,
% 0.60/0.64 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0)))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(212,plain,
% 0.60/0.64 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0)))))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(213,plain,
% 0.60/0.64 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.60/0.64 tff(214,plain,
% 0.60/0.64 (~(v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0)))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[213, 70, 210])).
% 0.60/0.64 tff(215,plain,
% 0.60/0.64 ((v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0))) | m2_lattice4(k19_filter_2(A!0, B!1), A!0)),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(216,plain,
% 0.60/0.64 (m2_lattice4(k19_filter_2(A!0, B!1), A!0)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.60/0.64 tff(217,plain,
% 0.60/0.64 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k19_filter_2(A!0, B!1), A!0)) | m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0)) | m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(218,plain,
% 0.60/0.64 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k19_filter_2(A!0, B!1), A!0)) | m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(219,plain,
% 0.60/0.64 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0)) | m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.60/0.64 tff(220,plain,
% 0.60/0.64 (m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[219, 99, 216])).
% 0.60/0.64 tff(221,plain,
% 0.60/0.64 ((v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m2_lattice4(k19_filter_2(A!0, B!1), A!0))) | (~v1_xboole_0(k19_filter_2(A!0, B!1)))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(222,plain,
% 0.60/0.64 (~v1_xboole_0(k19_filter_2(A!0, B!1))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[221, 214])).
% 0.60/0.64 tff(223,plain,
% 0.60/0.64 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D))))))))))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(224,plain,
% 0.60/0.64 ((v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, B!1), D)) | (~m2_filter_2(D, A!0)))))))))))) <=> (v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D))))))))))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(225,plain,
% 0.60/0.64 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, B!1), D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[224])).
% 0.60/0.65 tff(226,plain,
% 0.60/0.65 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, B!1), D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D))))))))))))),
% 0.60/0.65 inference(transitivity,[status(thm)],[225, 223])).
% 0.60/0.65 tff(227,plain,
% 0.60/0.65 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(k19_filter_2(A!0, B!1), D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(228,plain,
% 0.60/0.65 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.60/0.65 tff(229,plain,
% 0.60/0.65 ((~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[228, 141, 222])).
% 0.60/0.65 tff(230,plain,
% 0.60/0.65 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[229, 220])).
% 0.60/0.65 tff(231,plain,
% 0.60/0.65 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(232,plain,
% 0.60/0.65 (((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D))))))))))) <=> ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(233,plain,
% 0.60/0.65 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))))))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[232])).
% 0.60/0.65 tff(234,plain,
% 0.60/0.65 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))))))),
% 0.60/0.65 inference(transitivity,[status(thm)],[233, 231])).
% 0.60/0.65 tff(235,plain,
% 0.60/0.65 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(236,plain,
% 0.60/0.66 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (C = k19_filter_2(A!0, k19_filter_2(A!0, B!1))) | (~(r1_tarski(C, tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0))) | (~m2_filter_2(tptp_fun_D_4(C, k19_filter_2(A!0, B!1), A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | (~((~r1_tarski(k19_filter_2(A!0, B!1), C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(k19_filter_2(A!0, B!1), D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.60/0.66 tff(237,plain,
% 0.60/0.66 (~((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[236, 210, 230])).
% 0.60/0.66 tff(238,plain,
% 0.60/0.66 (((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))))) | ((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))),
% 0.60/0.66 inference(tautology,[status(thm)],[])).
% 0.60/0.66 tff(239,plain,
% 0.60/0.66 ((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.60/0.66 tff(240,plain,
% 0.60/0.66 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D))))))))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(241,plain,
% 0.60/0.66 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B!1, D)) | (~m2_filter_2(D, A!0)))))))))))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D))))))))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(242,plain,
% 0.60/0.66 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B!1, D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[241])).
% 0.60/0.66 tff(243,plain,
% 0.60/0.66 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B!1, D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D))))))))))))),
% 0.60/0.66 inference(transitivity,[status(thm)],[242, 240])).
% 0.60/0.66 tff(244,plain,
% 0.60/0.66 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B!1, D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(245,plain,
% 0.60/0.66 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.60/0.66 tff(246,plain,
% 0.60/0.66 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[245, 203, 202, 141])).
% 0.60/0.66 tff(247,plain,
% 0.60/0.66 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(248,plain,
% 0.60/0.66 (((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1)) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D))))))))))) <=> ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(249,plain,
% 0.60/0.66 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1)) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D)))))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[248])).
% 0.60/0.66 tff(250,plain,
% 0.60/0.66 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1)) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))))))),
% 0.60/0.66 inference(transitivity,[status(thm)],[249, 247])).
% 0.60/0.66 tff(251,plain,
% 0.60/0.66 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1)) | (~(r1_tarski(k19_filter_2(A!0, B!1), tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, B!1), B!1, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, B!1) = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, B!1), D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(252,plain,
% 0.60/0.66 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B!1, C)) | (C = k19_filter_2(A!0, B!1)) | (~(r1_tarski(C, tptp_fun_D_4(C, B!1, A!0)) | (~r1_tarski(B!1, tptp_fun_D_4(C, B!1, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B!1, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B!1))) | (~((~r1_tarski(B!1, C)) | (~![D: $i] : (r1_tarski(C, D) | (~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D)))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.60/0.66 tff(253,plain,
% 0.60/0.66 (~((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[252, 210, 246])).
% 0.60/0.66 tff(254,plain,
% 0.60/0.66 (((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D)))) | ![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))),
% 0.60/0.66 inference(tautology,[status(thm)],[])).
% 0.60/0.66 tff(255,plain,
% 0.60/0.66 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.60/0.66 tff(256,plain,
% 0.60/0.66 (((~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | (~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D)))) | r1_tarski(B!1, k19_filter_2(A!0, B!1))),
% 0.60/0.66 inference(tautology,[status(thm)],[])).
% 0.60/0.66 tff(257,plain,
% 0.60/0.66 (r1_tarski(B!1, k19_filter_2(A!0, B!1))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[256, 253])).
% 0.60/0.66 tff(258,plain,
% 0.60/0.66 (((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))) <=> ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(259,plain,
% 0.60/0.67 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))) | ((~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(260,plain,
% 0.60/0.67 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r1_tarski(B!1, D)) | r1_tarski(k19_filter_2(A!0, B!1), D))) | (~m2_filter_2(k19_filter_2(A!0, B!1), A!0)) | (~r1_tarski(B!1, k19_filter_2(A!0, B!1))) | r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.60/0.67 tff(261,plain,
% 0.60/0.67 (r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[260, 210, 257, 255])).
% 0.60/0.67 tff(262,plain,
% 0.60/0.67 ((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))),
% 0.60/0.67 inference(tautology,[status(thm)],[])).
% 0.60/0.67 tff(263,plain,
% 0.60/0.67 ((~((~r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))))) | (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1)))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.60/0.67 tff(264,plain,
% 0.60/0.67 (k19_filter_2(A!0, B!1) = k19_filter_2(A!0, k19_filter_2(A!0, B!1))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[263, 239])).
% 0.60/0.67 tff(265,plain,
% 0.60/0.67 (r1_tarski(k19_filter_2(A!0, B!1), k19_filter_2(A!0, B!1)) <=> r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[264])).
% 0.60/0.67 tff(266,plain,
% 0.60/0.67 (r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[261, 265])).
% 0.60/0.67 tff(267,plain,
% 0.60/0.67 ((~(~((~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) | (~r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))) <=> ((~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) | (~r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(268,plain,
% 0.60/0.67 ((((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))) <=> (~((~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) | (~r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(269,plain,
% 0.60/0.67 ((~(((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))) <=> (~(~((~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) | (~r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[268])).
% 0.60/0.67 tff(270,plain,
% 0.60/0.67 ((~(((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))) <=> ((~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) | (~r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1))))),
% 0.60/0.67 inference(transitivity,[status(thm)],[269, 267])).
% 0.60/0.67 tff(271,plain,
% 0.60/0.67 (~(((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) & r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))),
% 0.60/0.67 inference(or_elim,[status(thm)],[37])).
% 0.60/0.67 tff(272,plain,
% 0.60/0.67 ((~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) | (~r1_tarski(k19_filter_2(A!0, k19_filter_2(A!0, B!1)), k19_filter_2(A!0, B!1)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.60/0.67 tff(273,plain,
% 0.60/0.67 (~((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[272, 266])).
% 0.60/0.67 tff(274,plain,
% 0.60/0.67 (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) | (~r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))),
% 0.60/0.67 inference(tautology,[status(thm)],[])).
% 0.60/0.67 tff(275,plain,
% 0.60/0.67 (~r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[274, 273])).
% 0.60/0.67 tff(276,plain,
% 0.60/0.67 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.67 inference(and_elim,[status(thm)],[36])).
% 0.60/0.67 tff(277,plain,
% 0.60/0.67 (~v1_xboole_0(C!2)),
% 0.60/0.67 inference(and_elim,[status(thm)],[36])).
% 0.60/0.67 tff(278,plain,
% 0.60/0.67 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0))))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(279,plain,
% 0.60/0.67 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0))))))))))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(280,plain,
% 0.60/0.67 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(B, C)) | (C = k19_filter_2(A!0, B)) | (~(r1_tarski(C, tptp_fun_D_4(C, B, A!0)) | (~r1_tarski(B, tptp_fun_D_4(C, B, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, B, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, B))) | (~((~r1_tarski(B, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(B, D)) | (~m2_filter_2(D, A!0))))))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.60/0.67 tff(281,plain,
% 0.60/0.67 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[280, 277, 276, 141])).
% 0.60/0.67 tff(282,plain,
% 0.60/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(C!2) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(283,plain,
% 0.60/0.67 ((v3_struct_0(A!0) | v1_xboole_0(C!2) | m2_filter_2(k19_filter_2(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v1_xboole_0(C!2) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(284,plain,
% 0.60/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(C!2) | m2_filter_2(k19_filter_2(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0)))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[283])).
% 0.60/0.67 tff(285,plain,
% 0.60/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(C!2) | m2_filter_2(k19_filter_2(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(C!2) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))),
% 0.60/0.67 inference(transitivity,[status(thm)],[284, 282])).
% 0.60/0.67 tff(286,plain,
% 0.60/0.67 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(C!2) | m2_filter_2(k19_filter_2(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(287,plain,
% 0.60/0.67 ((~![A: $i, B: $i] : (v3_struct_0(A) | v1_xboole_0(B) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(C!2) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0)),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.60/0.67 tff(288,plain,
% 0.60/0.67 (m2_filter_2(k19_filter_2(A!0, C!2), A!0)),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[287, 43, 42, 41, 277, 276, 13])).
% 0.60/0.67 tff(289,plain,
% 0.60/0.67 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(290,plain,
% 0.60/0.67 (((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2)) | (~(r1_tarski(k19_filter_2(A!0, C!2), tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, C!2), D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0))))))))))) <=> ((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(291,plain,
% 0.60/0.67 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2)) | (~(r1_tarski(k19_filter_2(A!0, C!2), tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, C!2), D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D)))))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[290])).
% 0.60/0.67 tff(292,plain,
% 0.60/0.67 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2)) | (~(r1_tarski(k19_filter_2(A!0, C!2), tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, C!2), D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))))))),
% 0.60/0.67 inference(transitivity,[status(thm)],[291, 289])).
% 0.60/0.67 tff(293,plain,
% 0.60/0.67 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | ((~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2)) | (~(r1_tarski(k19_filter_2(A!0, C!2), tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(k19_filter_2(A!0, C!2), C!2, A!0), A!0)))))) | (~((~(k19_filter_2(A!0, C!2) = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : (r1_tarski(k19_filter_2(A!0, C!2), D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(294,plain,
% 0.60/0.68 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~((~((~r1_tarski(C!2, C)) | (C = k19_filter_2(A!0, C!2)) | (~(r1_tarski(C, tptp_fun_D_4(C, C!2, A!0)) | (~r1_tarski(C!2, tptp_fun_D_4(C, C!2, A!0))) | (~m2_filter_2(tptp_fun_D_4(C, C!2, A!0), A!0)))))) | (~((~(C = k19_filter_2(A!0, C!2))) | (~((~r1_tarski(C!2, C)) | (~![D: $i] : (r1_tarski(C, D) | (~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)))))))))))) | (~m2_filter_2(k19_filter_2(A!0, C!2), A!0)) | (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D)))))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.60/0.68 tff(295,plain,
% 0.60/0.68 (~((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[294, 288, 281])).
% 0.60/0.68 tff(296,plain,
% 0.60/0.68 (((~r1_tarski(C!2, k19_filter_2(A!0, C!2))) | (~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D)))) | ![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))),
% 0.60/0.68 inference(tautology,[status(thm)],[])).
% 0.60/0.68 tff(297,plain,
% 0.60/0.68 (![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.60/0.68 tff(298,plain,
% 0.60/0.68 (((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | (r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3))))) <=> ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(299,plain,
% 0.60/0.68 (((~r1_tarski(C!2, k19_filter_2(A!0, D!3))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) <=> (r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(300,plain,
% 0.60/0.68 (((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | ((~r1_tarski(C!2, k19_filter_2(A!0, D!3))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) <=> ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | (r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3)))))),
% 0.60/0.68 inference(monotonicity,[status(thm)],[299])).
% 0.60/0.68 tff(301,plain,
% 0.60/0.68 (((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | ((~r1_tarski(C!2, k19_filter_2(A!0, D!3))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))) <=> ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3))))),
% 0.60/0.68 inference(transitivity,[status(thm)],[300, 298])).
% 0.60/0.68 tff(302,plain,
% 0.60/0.68 ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | ((~r1_tarski(C!2, k19_filter_2(A!0, D!3))) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(303,plain,
% 0.60/0.68 ((~![D: $i] : ((~r1_tarski(C!2, D)) | (~m2_filter_2(D, A!0)) | r1_tarski(k19_filter_2(A!0, C!2), D))) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~m2_filter_2(k19_filter_2(A!0, D!3), A!0)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.60/0.68 tff(304,plain,
% 0.60/0.68 (r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3)) | (~r1_tarski(C!2, k19_filter_2(A!0, D!3)))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[303, 50, 297])).
% 0.60/0.68 tff(305,plain,
% 0.60/0.68 (~r1_tarski(C!2, k19_filter_2(A!0, D!3))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[304, 275])).
% 0.60/0.68 tff(306,plain,
% 0.60/0.68 (~r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[305, 201])).
% 0.60/0.68 tff(307,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(308,plain,
% 0.60/0.68 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1_tarski(A, B) & r1_tarski(B, C)) <=> (~((~r1_tarski(B, C)) | (~r1_tarski(A, B))))), ((~(r1_tarski(A, B) & r1_tarski(B, C))) <=> (~(~((~r1_tarski(B, C)) | (~r1_tarski(A, B))))))), rewrite((~(~((~r1_tarski(B, C)) | (~r1_tarski(A, B))))) <=> ((~r1_tarski(B, C)) | (~r1_tarski(A, B)))), ((~(r1_tarski(A, B) & r1_tarski(B, C))) <=> ((~r1_tarski(B, C)) | (~r1_tarski(A, B))))), (((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> (((~r1_tarski(B, C)) | (~r1_tarski(A, B))) | r1_tarski(A, C)))), rewrite((((~r1_tarski(B, C)) | (~r1_tarski(A, B))) | r1_tarski(A, C)) <=> (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))), (((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))))),
% 0.60/0.68 inference(bind,[status(th)],[])).
% 0.60/0.68 tff(309,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))),
% 0.60/0.68 inference(quant_intro,[status(thm)],[308])).
% 0.60/0.68 tff(310,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(311,plain,
% 0.60/0.68 (^[A: $i, B: $i, C: $i] : rewrite(((r1_tarski(A, B) & r1_tarski(B, C)) => r1_tarski(A, C)) <=> ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C)))),
% 0.60/0.68 inference(bind,[status(th)],[])).
% 0.60/0.68 tff(312,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : ((r1_tarski(A, B) & r1_tarski(B, C)) => r1_tarski(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.60/0.68 inference(quant_intro,[status(thm)],[311])).
% 0.60/0.68 tff(313,axiom,(![A: $i, B: $i, C: $i] : ((r1_tarski(A, B) & r1_tarski(B, C)) => r1_tarski(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.60/0.68 tff(314,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.60/0.68 tff(315,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[314, 310])).
% 0.60/0.68 tff(316,plain,(
% 0.60/0.68 ![A: $i, B: $i, C: $i] : ((~(r1_tarski(A, B) & r1_tarski(B, C))) | r1_tarski(A, C))),
% 0.60/0.68 inference(skolemize,[status(sab)],[315])).
% 0.60/0.68 tff(317,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[316, 309])).
% 0.60/0.68 tff(318,plain,
% 0.60/0.68 (![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[317, 307])).
% 0.60/0.68 tff(319,plain,
% 0.60/0.68 (((~r1_tarski(C!2, D!3)) | r1_tarski(k19_filter_2(A!0, C!2), k19_filter_2(A!0, D!3))) | r1_tarski(C!2, D!3)),
% 0.60/0.68 inference(tautology,[status(thm)],[])).
% 0.60/0.68 tff(320,plain,
% 0.60/0.68 (r1_tarski(C!2, D!3)),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[319, 273])).
% 0.60/0.68 tff(321,plain,
% 0.60/0.68 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | ((~r1_tarski(C!2, D!3)) | r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | (~r1_tarski(C!2, D!3)) | r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(322,plain,
% 0.60/0.68 ((r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~r1_tarski(C!2, D!3))) <=> ((~r1_tarski(C!2, D!3)) | r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))))),
% 0.60/0.68 inference(rewrite,[status(thm)],[])).
% 0.60/0.68 tff(323,plain,
% 0.60/0.68 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | (r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~r1_tarski(C!2, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | ((~r1_tarski(C!2, D!3)) | r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3))))))),
% 0.60/0.68 inference(monotonicity,[status(thm)],[322])).
% 0.60/0.68 tff(324,plain,
% 0.60/0.68 (((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | (r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~r1_tarski(C!2, D!3)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | (~r1_tarski(C!2, D!3)) | r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))))),
% 0.60/0.68 inference(transitivity,[status(thm)],[323, 321])).
% 0.60/0.68 tff(325,plain,
% 0.60/0.68 ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | (r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3)))) | (~r1_tarski(C!2, D!3)))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(326,plain,
% 0.60/0.68 ((~![A: $i, B: $i, C: $i] : (r1_tarski(A, C) | (~r1_tarski(B, C)) | (~r1_tarski(A, B)))) | (~r1_tarski(C!2, D!3)) | r1_tarski(C!2, k19_filter_2(A!0, k19_filter_2(A!0, D!3))) | (~r1_tarski(D!3, k19_filter_2(A!0, k19_filter_2(A!0, D!3))))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.60/0.68 tff(327,plain,
% 0.60/0.68 ($false),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[326, 320, 318, 306, 198])).
% 0.60/0.68 % SZS output end Proof
%------------------------------------------------------------------------------