TSTP Solution File: LAT329+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT329+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:08 EDT 2022
% Result : Theorem 6.41s 4.38s
% Output : Proof 6.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT329+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 14:39:17 EDT 2022
% 0.12/0.34 % 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.
% 6.41/4.38 % SZS status Theorem
% 6.41/4.38 % SZS output start Proof
% 6.41/4.38 tff(r3_lattices_type, type, (
% 6.41/4.38 r3_lattices: ( $i * $i * $i ) > $o)).
% 6.41/4.38 tff(tptp_fun_D_2_type, type, (
% 6.41/4.38 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 6.41/4.38 tff(u1_struct_0_type, type, (
% 6.41/4.38 u1_struct_0: $i > $i)).
% 6.41/4.38 tff(tptp_fun_A_0_type, type, (
% 6.41/4.38 tptp_fun_A_0: $i)).
% 6.41/4.38 tff(k22_filter_2_type, type, (
% 6.41/4.38 k22_filter_2: ( $i * $i * $i ) > $i)).
% 6.41/4.38 tff(k6_lattices_type, type, (
% 6.41/4.38 k6_lattices: $i > $i)).
% 6.41/4.38 tff(tptp_fun_B_1_type, type, (
% 6.41/4.38 tptp_fun_B_1: $i)).
% 6.41/4.38 tff(k2_filter_0_type, type, (
% 6.41/4.38 k2_filter_0: ( $i * $i ) > $i)).
% 6.41/4.38 tff(tptp_fun_D_11_type, type, (
% 6.41/4.38 tptp_fun_D_11: ( $i * $i * $i ) > $i)).
% 6.41/4.38 tff(m1_subset_1_type, type, (
% 6.41/4.38 m1_subset_1: ( $i * $i ) > $o)).
% 6.41/4.38 tff(r2_hidden_type, type, (
% 6.41/4.38 r2_hidden: ( $i * $i ) > $o)).
% 6.41/4.38 tff(a_2_0_filter_0_type, type, (
% 6.41/4.38 a_2_0_filter_0: ( $i * $i ) > $i)).
% 6.41/4.38 tff(l3_lattices_type, type, (
% 6.41/4.38 l3_lattices: $i > $o)).
% 6.41/4.38 tff(v10_lattices_type, type, (
% 6.41/4.38 v10_lattices: $i > $o)).
% 6.41/4.38 tff(v3_struct_0_type, type, (
% 6.41/4.38 v3_struct_0: $i > $o)).
% 6.41/4.38 tff(r1_filter_2_type, type, (
% 6.41/4.38 r1_filter_2: ( $i * $i * $i ) > $o)).
% 6.41/4.38 tff(k2_filter_2_type, type, (
% 6.41/4.38 k2_filter_2: ( $i * $i ) > $i)).
% 6.41/4.38 tff(v14_lattices_type, type, (
% 6.41/4.38 v14_lattices: $i > $o)).
% 6.41/4.38 tff(l2_lattices_type, type, (
% 6.41/4.38 l2_lattices: $i > $o)).
% 6.41/4.38 tff(l1_lattices_type, type, (
% 6.41/4.38 l1_lattices: $i > $o)).
% 6.41/4.38 tff(v9_lattices_type, type, (
% 6.41/4.38 v9_lattices: $i > $o)).
% 6.41/4.38 tff(v8_lattices_type, type, (
% 6.41/4.38 v8_lattices: $i > $o)).
% 6.41/4.38 tff(v7_lattices_type, type, (
% 6.41/4.38 v7_lattices: $i > $o)).
% 6.41/4.38 tff(v6_lattices_type, type, (
% 6.41/4.38 v6_lattices: $i > $o)).
% 6.41/4.38 tff(v5_lattices_type, type, (
% 6.41/4.38 v5_lattices: $i > $o)).
% 6.41/4.38 tff(v4_lattices_type, type, (
% 6.41/4.38 v4_lattices: $i > $o)).
% 6.41/4.38 tff(k1_zfmisc_1_type, type, (
% 6.41/4.38 k1_zfmisc_1: $i > $i)).
% 6.41/4.38 tff(v1_xboole_0_type, type, (
% 6.41/4.38 v1_xboole_0: $i > $o)).
% 6.41/4.38 tff(l1_struct_0_type, type, (
% 6.41/4.38 l1_struct_0: $i > $o)).
% 6.41/4.38 tff(m2_lattice4_type, type, (
% 6.41/4.38 m2_lattice4: ( $i * $i ) > $o)).
% 6.41/4.38 tff(m1_filter_0_type, type, (
% 6.41/4.38 m1_filter_0: ( $i * $i ) > $o)).
% 6.41/4.38 tff(1,plain,
% 6.41/4.38 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))))),
% 6.41/4.38 inference(bind,[status(th)],[])).
% 6.41/4.38 tff(2,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))),
% 6.41/4.38 inference(quant_intro,[status(thm)],[1])).
% 6.41/4.38 tff(3,plain,
% 6.41/4.38 (^[A: $i, B: $i, C: $i] : rewrite((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))))),
% 6.41/4.38 inference(bind,[status(th)],[])).
% 6.41/4.38 tff(4,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))),
% 6.41/4.38 inference(quant_intro,[status(thm)],[3])).
% 6.41/4.38 tff(5,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))),
% 6.41/4.38 inference(transitivity,[status(thm)],[4, 2])).
% 6.41/4.38 tff(6,plain,
% 6.41/4.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) <=> (~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))))), rewrite((~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), trans(monotonicity(rewrite(((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) <=> ((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))), rewrite((r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))) <=> (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))), ((((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))) <=> (((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A)))))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))), rewrite((((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A)))))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))) <=> (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))), ((((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))) <=> (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))))) <=> ((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))))), rewrite(((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D)))))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))))),
% 6.41/4.38 inference(bind,[status(th)],[])).
% 6.41/4.38 tff(7,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))),
% 6.41/4.38 inference(quant_intro,[status(thm)],[6])).
% 6.41/4.38 tff(8,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))),
% 6.41/4.38 inference(rewrite,[status(thm)],[])).
% 6.41/4.38 tff(9,plain,
% 6.41/4.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))))), rewrite((r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, C, D))) <=> (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, C, D)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, C, D)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))))),
% 6.41/4.38 inference(bind,[status(th)],[])).
% 6.41/4.38 tff(10,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, C, D)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))),
% 6.41/4.38 inference(quant_intro,[status(thm)],[9])).
% 6.41/4.38 tff(11,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, C, D))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fraenkel_a_2_0_filter_0')).
% 6.41/4.38 tff(12,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))),
% 6.41/4.38 inference(modus_ponens,[status(thm)],[11, 10])).
% 6.41/4.38 tff(13,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_0(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))),
% 6.41/4.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 6.41/4.38 tff(14,plain,(
% 6.41/4.38 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_0(B, C))) | (m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_11(C, B, A)) & r3_lattices(B, C, tptp_fun_D_11(C, B, A)))) & (r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, C, D))))))),
% 6.41/4.38 inference(skolemize,[status(sab)],[13])).
% 6.41/4.38 tff(15,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))),
% 6.41/4.38 inference(modus_ponens,[status(thm)],[14, 7])).
% 6.41/4.38 tff(16,plain,
% 6.41/4.38 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))),
% 6.41/4.38 inference(modus_ponens,[status(thm)],[15, 5])).
% 6.41/4.38 tff(17,plain,
% 6.41/4.38 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 6.41/4.38 inference(rewrite,[status(thm)],[])).
% 6.41/4.38 tff(18,plain,
% 6.41/4.38 ((~(r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 6.41/4.38 inference(rewrite,[status(thm)],[])).
% 6.41/4.38 tff(19,plain,
% 6.41/4.38 ((~(~((~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))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(20,plain,
% 6.41/4.39 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & (~(r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 6.41/4.39 inference(monotonicity,[status(thm)],[19, 18])).
% 6.41/4.39 tff(21,plain,
% 6.41/4.39 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & (~(r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 6.41/4.39 inference(transitivity,[status(thm)],[20, 17])).
% 6.41/4.39 tff(22,plain,
% 6.41/4.39 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(23,plain,
% 6.41/4.39 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(24,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t66_filter_2')).
% 6.41/4.39 tff(25,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 6.41/4.39 tff(26,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[25, 22])).
% 6.41/4.39 tff(27,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[26, 22])).
% 6.41/4.39 tff(28,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[27, 22])).
% 6.41/4.39 tff(29,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[28, 22])).
% 6.41/4.39 tff(30,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 6.41/4.39 tff(31,plain,
% 6.41/4.39 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[30, 22])).
% 6.41/4.39 tff(32,plain,
% 6.41/4.39 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 6.41/4.39 tff(33,plain,
% 6.41/4.39 (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 6.41/4.39 inference(and_elim,[status(thm)],[32])).
% 6.41/4.39 tff(34,plain,
% 6.41/4.39 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 6.41/4.39 inference(or_elim,[status(thm)],[33])).
% 6.41/4.39 tff(35,plain,
% 6.41/4.39 (l3_lattices(A!0)),
% 6.41/4.39 inference(and_elim,[status(thm)],[32])).
% 6.41/4.39 tff(36,plain,
% 6.41/4.39 (v10_lattices(A!0)),
% 6.41/4.39 inference(and_elim,[status(thm)],[32])).
% 6.41/4.39 tff(37,plain,
% 6.41/4.39 (~v3_struct_0(A!0)),
% 6.41/4.39 inference(and_elim,[status(thm)],[32])).
% 6.41/4.39 tff(38,plain,
% 6.41/4.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(39,plain,
% 6.41/4.39 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D)))))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(40,plain,
% 6.41/4.39 ((~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, B!1, D))))))) <=> (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D)))))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(41,plain,
% 6.41/4.39 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, B!1, D)))))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))))),
% 6.41/4.39 inference(monotonicity,[status(thm)],[40])).
% 6.41/4.39 tff(42,plain,
% 6.41/4.39 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, B!1, D)))))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))))),
% 6.41/4.39 inference(transitivity,[status(thm)],[41, 39])).
% 6.41/4.39 tff(43,plain,
% 6.41/4.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, B!1, D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D)))))))))),
% 6.41/4.39 inference(monotonicity,[status(thm)],[42])).
% 6.41/4.39 tff(44,plain,
% 6.41/4.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, B!1, D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))))),
% 6.41/4.39 inference(transitivity,[status(thm)],[43, 38])).
% 6.41/4.39 tff(45,plain,
% 6.41/4.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, B!1, D))))))))),
% 6.41/4.39 inference(quant_inst,[status(thm)],[])).
% 6.41/4.39 tff(46,plain,
% 6.41/4.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D)))))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 6.41/4.39 tff(47,plain,
% 6.41/4.39 (~((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D))))))),
% 6.41/4.39 inference(unit_resolution,[status(thm)],[46, 37, 36, 35, 34, 16])).
% 6.41/4.39 tff(48,plain,
% 6.41/4.39 (((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~(r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, D)) | (~(B!1 = D)))))) | ((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))),
% 6.41/4.39 inference(tautology,[status(thm)],[])).
% 6.41/4.39 tff(49,plain,
% 6.41/4.39 ((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1)))))),
% 6.41/4.39 inference(unit_resolution,[status(thm)],[48, 47])).
% 6.41/4.39 tff(50,plain,
% 6.41/4.39 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))))),
% 6.41/4.39 inference(bind,[status(th)],[])).
% 6.41/4.39 tff(51,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(quant_intro,[status(thm)],[50])).
% 6.41/4.39 tff(52,plain,
% 6.41/4.39 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))))),
% 6.41/4.39 inference(bind,[status(th)],[])).
% 6.41/4.39 tff(53,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))),
% 6.41/4.39 inference(quant_intro,[status(thm)],[52])).
% 6.41/4.39 tff(54,plain,
% 6.41/4.39 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))))),
% 6.41/4.39 inference(bind,[status(th)],[])).
% 6.41/4.39 tff(55,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))),
% 6.41/4.39 inference(quant_intro,[status(thm)],[54])).
% 6.41/4.39 tff(56,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))),
% 6.41/4.39 inference(transitivity,[status(thm)],[55, 53])).
% 6.41/4.39 tff(57,plain,
% 6.41/4.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))))),
% 6.41/4.39 inference(bind,[status(th)],[])).
% 6.41/4.39 tff(58,plain,
% 6.41/4.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))),
% 6.41/4.39 inference(quant_intro,[status(thm)],[57])).
% 6.41/4.39 tff(59,plain,
% 6.41/4.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(60,plain,
% 6.41/4.39 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))))),
% 6.41/4.39 inference(bind,[status(th)],[])).
% 6.41/4.39 tff(61,plain,
% 6.41/4.39 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k2_filter_0(A, B) = a_2_0_filter_0(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(quant_intro,[status(thm)],[60])).
% 6.41/4.39 tff(62,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_filter_0')).
% 6.41/4.39 tff(63,plain,
% 6.41/4.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 6.41/4.39 tff(64,plain,
% 6.41/4.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 6.41/4.39 tff(65,plain,(
% 6.41/4.39 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(skolemize,[status(sab)],[64])).
% 6.41/4.39 tff(66,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 6.41/4.39 tff(67,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))) | (~v10_lattices(A)))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[66, 56])).
% 6.41/4.39 tff(68,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[67, 51])).
% 6.41/4.39 tff(69,plain,
% 6.41/4.39 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B))))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(70,plain,
% 6.41/4.39 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B))))),
% 6.41/4.39 inference(quant_inst,[status(thm)],[])).
% 6.41/4.39 tff(71,plain,
% 6.41/4.39 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k2_filter_0(A, B) = a_2_0_filter_0(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 6.41/4.39 tff(72,plain,
% 6.41/4.39 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))),
% 6.41/4.39 inference(unit_resolution,[status(thm)],[71, 37, 36, 35, 68])).
% 6.41/4.39 tff(73,plain,
% 6.41/4.39 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_filter_0(A!0, B!1) = a_2_0_filter_0(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_filter_0(A!0, B!1) = a_2_0_filter_0(A!0, B!1)))),
% 6.41/4.39 inference(rewrite,[status(thm)],[])).
% 6.41/4.39 tff(74,plain,
% 6.41/4.39 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_filter_0(A!0, B!1) = a_2_0_filter_0(A!0, B!1)))),
% 6.41/4.39 inference(quant_inst,[status(thm)],[])).
% 6.41/4.39 tff(75,plain,
% 6.41/4.39 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_filter_0(A!0, B!1) = a_2_0_filter_0(A!0, B!1))),
% 6.41/4.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 6.41/4.39 tff(76,plain,
% 6.41/4.39 (k2_filter_0(A!0, B!1) = a_2_0_filter_0(A!0, B!1)),
% 6.41/4.39 inference(unit_resolution,[status(thm)],[75, 34, 72])).
% 6.41/4.39 tff(77,plain,
% 6.41/4.39 (a_2_0_filter_0(A!0, B!1) = k2_filter_0(A!0, B!1)),
% 6.41/4.39 inference(symmetry,[status(thm)],[76])).
% 6.41/4.39 tff(78,plain,
% 6.41/4.39 (r2_hidden(B!1, a_2_0_filter_0(A!0, B!1)) <=> r2_hidden(B!1, k2_filter_0(A!0, B!1))),
% 6.41/4.39 inference(monotonicity,[status(thm)],[77])).
% 6.41/4.39 tff(79,plain,
% 6.41/4.39 (r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))),
% 6.41/4.39 inference(symmetry,[status(thm)],[78])).
% 6.41/4.39 tff(80,plain,
% 6.41/4.39 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))),
% 6.41/4.39 inference(bind,[status(th)],[])).
% 6.41/4.39 tff(81,plain,
% 6.41/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.41/4.39 inference(quant_intro,[status(thm)],[80])).
% 6.41/4.39 tff(82,plain,
% 6.41/4.39 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))))),
% 6.44/4.39 inference(bind,[status(th)],[])).
% 6.44/4.39 tff(83,plain,
% 6.44/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 6.44/4.39 inference(quant_intro,[status(thm)],[82])).
% 6.44/4.39 tff(84,plain,
% 6.44/4.39 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))))),
% 6.44/4.39 inference(bind,[status(th)],[])).
% 6.44/4.39 tff(85,plain,
% 6.44/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 6.44/4.39 inference(quant_intro,[status(thm)],[84])).
% 6.44/4.39 tff(86,plain,
% 6.44/4.39 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 6.44/4.39 inference(transitivity,[status(thm)],[85, 83])).
% 6.44/4.39 tff(87,plain,
% 6.44/4.39 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))))),
% 6.44/4.39 inference(bind,[status(th)],[])).
% 6.44/4.39 tff(88,plain,
% 6.44/4.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 6.44/4.39 inference(quant_intro,[status(thm)],[87])).
% 6.44/4.39 tff(89,plain,
% 6.44/4.39 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(90,plain,
% 6.44/4.40 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(91,plain,
% 6.44/4.40 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[90])).
% 6.44/4.40 tff(92,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_filter_0')).
% 6.44/4.40 tff(93,plain,
% 6.44/4.40 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 6.44/4.40 tff(94,plain,
% 6.44/4.40 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[93, 89])).
% 6.44/4.40 tff(95,plain,(
% 6.44/4.40 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.44/4.40 inference(skolemize,[status(sab)],[94])).
% 6.44/4.40 tff(96,plain,
% 6.44/4.40 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[95, 88])).
% 6.44/4.40 tff(97,plain,
% 6.44/4.40 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[96, 86])).
% 6.44/4.40 tff(98,plain,
% 6.44/4.40 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[97, 81])).
% 6.44/4.40 tff(99,plain,
% 6.44/4.40 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B)))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(100,plain,
% 6.44/4.40 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B)))))),
% 6.44/4.40 inference(quant_inst,[status(thm)],[])).
% 6.44/4.40 tff(101,plain,
% 6.44/4.40 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 6.44/4.40 tff(102,plain,
% 6.44/4.40 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[101, 37, 36, 35, 98])).
% 6.44/4.40 tff(103,plain,
% 6.44/4.40 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(104,plain,
% 6.44/4.40 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1))))),
% 6.44/4.40 inference(quant_inst,[status(thm)],[])).
% 6.44/4.40 tff(105,plain,
% 6.44/4.40 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 6.44/4.40 tff(106,plain,
% 6.44/4.40 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1)))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[105, 34, 102])).
% 6.44/4.40 tff(107,plain,
% 6.44/4.40 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, B!1)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, B!1)))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(108,plain,
% 6.44/4.40 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, B!1)))),
% 6.44/4.40 inference(quant_inst,[status(thm)],[])).
% 6.44/4.40 tff(109,plain,
% 6.44/4.40 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B!1)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, B!1))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 6.44/4.40 tff(110,plain,
% 6.44/4.40 (r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, B!1)),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[109, 34, 106])).
% 6.44/4.40 tff(111,plain,
% 6.44/4.40 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(112,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[111])).
% 6.44/4.40 tff(113,plain,
% 6.44/4.40 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(114,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[113])).
% 6.44/4.40 tff(115,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(116,plain,
% 6.44/4.40 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(117,plain,
% 6.44/4.40 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[116])).
% 6.44/4.40 tff(118,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 6.44/4.40 tff(119,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 6.44/4.40 tff(120,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[119, 115])).
% 6.44/4.40 tff(121,plain,(
% 6.44/4.40 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 6.44/4.40 inference(skolemize,[status(sab)],[120])).
% 6.44/4.40 tff(122,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[121, 114])).
% 6.44/4.40 tff(123,plain,
% 6.44/4.40 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[122, 112])).
% 6.44/4.40 tff(124,plain,
% 6.44/4.40 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(125,plain,
% 6.44/4.40 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 6.44/4.40 inference(quant_inst,[status(thm)],[])).
% 6.44/4.40 tff(126,plain,
% 6.44/4.40 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 6.44/4.40 tff(127,plain,
% 6.44/4.40 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[126, 35, 123])).
% 6.44/4.40 tff(128,plain,
% 6.44/4.40 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 6.44/4.40 inference(tautology,[status(thm)],[])).
% 6.44/4.40 tff(129,plain,
% 6.44/4.40 (l2_lattices(A!0)),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[128, 127])).
% 6.44/4.40 tff(130,plain,
% 6.44/4.40 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(131,plain,
% 6.44/4.40 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[130])).
% 6.44/4.40 tff(132,plain,
% 6.44/4.40 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A))))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(133,plain,
% 6.44/4.40 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[132])).
% 6.44/4.40 tff(134,plain,
% 6.44/4.40 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(135,plain,
% 6.44/4.40 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))),
% 6.44/4.40 inference(bind,[status(th)],[])).
% 6.44/4.40 tff(136,plain,
% 6.44/4.40 (![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 6.44/4.40 inference(quant_intro,[status(thm)],[135])).
% 6.44/4.40 tff(137,axiom,(![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_lattices')).
% 6.44/4.40 tff(138,plain,
% 6.44/4.40 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[137, 136])).
% 6.44/4.40 tff(139,plain,
% 6.44/4.40 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[138, 134])).
% 6.44/4.40 tff(140,plain,(
% 6.44/4.40 ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 6.44/4.40 inference(skolemize,[status(sab)],[139])).
% 6.44/4.40 tff(141,plain,
% 6.44/4.40 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[140, 133])).
% 6.44/4.40 tff(142,plain,
% 6.44/4.40 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[141, 131])).
% 6.44/4.40 tff(143,plain,
% 6.44/4.40 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(144,plain,
% 6.44/4.40 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))),
% 6.44/4.40 inference(quant_inst,[status(thm)],[])).
% 6.44/4.40 tff(145,plain,
% 6.44/4.40 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 6.44/4.40 tff(146,plain,
% 6.44/4.40 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[145, 37, 142])).
% 6.44/4.40 tff(147,plain,
% 6.44/4.40 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[146, 129])).
% 6.44/4.40 tff(148,plain,
% 6.44/4.40 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(149,plain,
% 6.44/4.40 ((v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D)))))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(150,plain,
% 6.44/4.40 ((~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k6_lattices(A!0) = D)) | (~r3_lattices(A!0, k6_lattices(A!0), D))))))) <=> (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D)))))))),
% 6.44/4.40 inference(rewrite,[status(thm)],[])).
% 6.44/4.40 tff(151,plain,
% 6.44/4.40 ((v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k6_lattices(A!0) = D)) | (~r3_lattices(A!0, k6_lattices(A!0), D)))))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))))),
% 6.44/4.40 inference(monotonicity,[status(thm)],[150])).
% 6.44/4.40 tff(152,plain,
% 6.44/4.40 ((v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k6_lattices(A!0) = D)) | (~r3_lattices(A!0, k6_lattices(A!0), D)))))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))))),
% 6.44/4.40 inference(transitivity,[status(thm)],[151, 149])).
% 6.44/4.40 tff(153,plain,
% 6.44/4.40 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k6_lattices(A!0) = D)) | (~r3_lattices(A!0, k6_lattices(A!0), D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D)))))))))),
% 6.44/4.40 inference(monotonicity,[status(thm)],[152])).
% 6.44/4.40 tff(154,plain,
% 6.44/4.40 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k6_lattices(A!0) = D)) | (~r3_lattices(A!0, k6_lattices(A!0), D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))))),
% 6.44/4.40 inference(transitivity,[status(thm)],[153, 148])).
% 6.44/4.40 tff(155,plain,
% 6.44/4.40 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k6_lattices(A!0) = D)) | (~r3_lattices(A!0, k6_lattices(A!0), D))))))))),
% 6.44/4.40 inference(quant_inst,[status(thm)],[])).
% 6.44/4.40 tff(156,plain,
% 6.44/4.40 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_0(B, C))) | (~((~m1_subset_1(tptp_fun_D_11(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_11(C, B, A))) | (~r3_lattices(B, C, tptp_fun_D_11(C, B, A))))))) | (~(r2_hidden(A, a_2_0_filter_0(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, C, D))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D)))))))),
% 6.44/4.40 inference(modus_ponens,[status(thm)],[155, 154])).
% 6.44/4.40 tff(157,plain,
% 6.44/4.40 (~((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D))))))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[156, 37, 36, 35, 16, 147])).
% 6.44/4.40 tff(158,plain,
% 6.44/4.40 (((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~(r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), D)) | (~(k6_lattices(A!0) = D)))))) | ((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))),
% 6.44/4.40 inference(tautology,[status(thm)],[])).
% 6.44/4.40 tff(159,plain,
% 6.44/4.40 ((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0))))))),
% 6.44/4.40 inference(unit_resolution,[status(thm)],[158, 157])).
% 6.44/4.40 tff(160,plain,
% 6.44/4.40 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (k2_filter_0(A!0, k6_lattices(A!0)) = a_2_0_filter_0(A!0, k6_lattices(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (k2_filter_0(A!0, k6_lattices(A!0)) = a_2_0_filter_0(A!0, k6_lattices(A!0))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(161,plain,
% 6.44/4.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (k2_filter_0(A!0, k6_lattices(A!0)) = a_2_0_filter_0(A!0, k6_lattices(A!0))))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(162,plain,
% 6.44/4.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k2_filter_0(A!0, B) = a_2_0_filter_0(A!0, B)))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (k2_filter_0(A!0, k6_lattices(A!0)) = a_2_0_filter_0(A!0, k6_lattices(A!0)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[161, 160])).
% 6.44/4.41 tff(163,plain,
% 6.44/4.41 (k2_filter_0(A!0, k6_lattices(A!0)) = a_2_0_filter_0(A!0, k6_lattices(A!0))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[162, 147, 72])).
% 6.44/4.41 tff(164,plain,
% 6.44/4.41 (a_2_0_filter_0(A!0, k6_lattices(A!0)) = k2_filter_0(A!0, k6_lattices(A!0))),
% 6.44/4.41 inference(symmetry,[status(thm)],[163])).
% 6.44/4.41 tff(165,plain,
% 6.44/4.41 (r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0))) <=> r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0)))),
% 6.44/4.41 inference(monotonicity,[status(thm)],[164])).
% 6.44/4.41 tff(166,plain,
% 6.44/4.41 (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))),
% 6.44/4.41 inference(symmetry,[status(thm)],[165])).
% 6.44/4.41 tff(167,plain,
% 6.44/4.41 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0)))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(168,plain,
% 6.44/4.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0)))))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(169,plain,
% 6.44/4.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0))))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[168, 167])).
% 6.44/4.41 tff(170,plain,
% 6.44/4.41 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0))))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[169, 102, 147])).
% 6.44/4.41 tff(171,plain,
% 6.44/4.41 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(172,plain,
% 6.44/4.41 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0))))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(173,plain,
% 6.44/4.41 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, k6_lattices(A!0))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 6.44/4.41 tff(174,plain,
% 6.44/4.41 (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[173, 147, 170])).
% 6.44/4.41 tff(175,plain,
% 6.44/4.41 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(176,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[175])).
% 6.44/4.41 tff(177,plain,
% 6.44/4.41 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(178,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[177])).
% 6.44/4.41 tff(179,plain,
% 6.44/4.41 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(180,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[179])).
% 6.44/4.41 tff(181,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 6.44/4.41 inference(transitivity,[status(thm)],[180, 178])).
% 6.44/4.41 tff(182,plain,
% 6.44/4.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(183,plain,
% 6.44/4.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[182])).
% 6.44/4.41 tff(184,plain,
% 6.44/4.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(185,plain,
% 6.44/4.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(186,plain,
% 6.44/4.41 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[185])).
% 6.44/4.41 tff(187,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_lattices')).
% 6.44/4.41 tff(188,plain,
% 6.44/4.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[187, 186])).
% 6.44/4.41 tff(189,plain,
% 6.44/4.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[188, 184])).
% 6.44/4.41 tff(190,plain,(
% 6.44/4.41 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(skolemize,[status(sab)],[189])).
% 6.44/4.41 tff(191,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[190, 183])).
% 6.44/4.41 tff(192,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[191, 181])).
% 6.44/4.41 tff(193,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[192, 176])).
% 6.44/4.41 tff(194,plain,
% 6.44/4.41 (v14_lattices(A!0)),
% 6.44/4.41 inference(or_elim,[status(thm)],[33])).
% 6.44/4.41 tff(195,plain,
% 6.44/4.41 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(196,plain,
% 6.44/4.41 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0))))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(197,plain,
% 6.44/4.41 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[196, 195])).
% 6.44/4.41 tff(198,plain,
% 6.44/4.41 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[197, 37, 36, 35, 194, 193])).
% 6.44/4.41 tff(199,plain,
% 6.44/4.41 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(200,plain,
% 6.44/4.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(201,plain,
% 6.44/4.41 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[200, 199])).
% 6.44/4.41 tff(202,plain,
% 6.44/4.41 (r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[201, 198, 147])).
% 6.44/4.41 tff(203,plain,
% 6.44/4.41 ((~(r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))) | r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) | (~r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))),
% 6.44/4.41 inference(tautology,[status(thm)],[])).
% 6.44/4.41 tff(204,plain,
% 6.44/4.41 ((~(r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0))) <=> r3_lattices(A!0, k6_lattices(A!0), k6_lattices(A!0)))) | r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0)))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[203, 202])).
% 6.44/4.41 tff(205,plain,
% 6.44/4.41 (r2_hidden(k6_lattices(A!0), k2_filter_0(A!0, k6_lattices(A!0)))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[204, 174])).
% 6.44/4.41 tff(206,plain,
% 6.44/4.41 (r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[205, 166])).
% 6.44/4.41 tff(207,plain,
% 6.44/4.41 ((~((~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))))) | (~r2_hidden(k6_lattices(A!0), a_2_0_filter_0(A!0, k6_lattices(A!0)))) | (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0))))))),
% 6.44/4.41 inference(tautology,[status(thm)],[])).
% 6.44/4.41 tff(208,plain,
% 6.44/4.41 (~((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[207, 206, 159])).
% 6.44/4.41 tff(209,plain,
% 6.44/4.41 (((~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~(k6_lattices(A!0) = tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)))) | (~r3_lattices(A!0, k6_lattices(A!0), tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0))))) | m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))),
% 6.44/4.41 inference(tautology,[status(thm)],[])).
% 6.44/4.41 tff(210,plain,
% 6.44/4.41 (m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[209, 208])).
% 6.44/4.41 tff(211,plain,
% 6.44/4.41 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(212,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[211])).
% 6.44/4.41 tff(213,plain,
% 6.44/4.41 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))))), rewrite(((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(214,plain,
% 6.44/4.41 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[213])).
% 6.44/4.41 tff(215,plain,
% 6.44/4.41 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(216,plain,
% 6.44/4.41 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(217,plain,
% 6.44/4.41 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[216])).
% 6.44/4.41 tff(218,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_lattices')).
% 6.44/4.41 tff(219,plain,
% 6.44/4.41 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[218, 217])).
% 6.44/4.41 tff(220,plain,
% 6.44/4.41 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[219, 215])).
% 6.44/4.41 tff(221,plain,(
% 6.44/4.41 ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 6.44/4.41 inference(skolemize,[status(sab)],[220])).
% 6.44/4.41 tff(222,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[221, 214])).
% 6.44/4.41 tff(223,plain,
% 6.44/4.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[222, 212])).
% 6.44/4.41 tff(224,plain,
% 6.44/4.41 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(225,plain,
% 6.44/4.41 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(226,plain,
% 6.44/4.41 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 6.44/4.41 inference(monotonicity,[status(thm)],[225])).
% 6.44/4.41 tff(227,plain,
% 6.44/4.41 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 6.44/4.41 inference(transitivity,[status(thm)],[226, 224])).
% 6.44/4.41 tff(228,plain,
% 6.44/4.41 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(229,plain,
% 6.44/4.41 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[228, 227])).
% 6.44/4.41 tff(230,plain,
% 6.44/4.41 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[229, 37, 36, 35, 223])).
% 6.44/4.41 tff(231,plain,
% 6.44/4.41 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v9_lattices(A!0)),
% 6.44/4.41 inference(tautology,[status(thm)],[])).
% 6.44/4.41 tff(232,plain,
% 6.44/4.41 (v9_lattices(A!0)),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[231, 230])).
% 6.44/4.41 tff(233,plain,
% 6.44/4.41 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v8_lattices(A!0)),
% 6.44/4.41 inference(tautology,[status(thm)],[])).
% 6.44/4.41 tff(234,plain,
% 6.44/4.41 (v8_lattices(A!0)),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[233, 230])).
% 6.44/4.41 tff(235,plain,
% 6.44/4.41 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 6.44/4.41 inference(tautology,[status(thm)],[])).
% 6.44/4.41 tff(236,plain,
% 6.44/4.41 (v6_lattices(A!0)),
% 6.44/4.41 inference(unit_resolution,[status(thm)],[235, 230])).
% 6.44/4.41 tff(237,plain,
% 6.44/4.41 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(238,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[237])).
% 6.44/4.41 tff(239,plain,
% 6.44/4.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))) | r3_lattices(A, B, B)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))) | r3_lattices(A, B, B)) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(240,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[239])).
% 6.44/4.41 tff(241,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(242,plain,
% 6.44/4.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))))),
% 6.44/4.41 inference(bind,[status(th)],[])).
% 6.44/4.41 tff(243,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 6.44/4.41 inference(quant_intro,[status(thm)],[242])).
% 6.44/4.41 tff(244,axiom,(![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r3_lattices')).
% 6.44/4.41 tff(245,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[244, 243])).
% 6.44/4.41 tff(246,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[245, 241])).
% 6.44/4.41 tff(247,plain,(
% 6.44/4.41 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 6.44/4.41 inference(skolemize,[status(sab)],[246])).
% 6.44/4.41 tff(248,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[247, 240])).
% 6.44/4.41 tff(249,plain,
% 6.44/4.41 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))),
% 6.44/4.41 inference(modus_ponens,[status(thm)],[248, 238])).
% 6.44/4.41 tff(250,plain,
% 6.44/4.41 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(251,plain,
% 6.44/4.41 ((v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.44/4.41 inference(rewrite,[status(thm)],[])).
% 6.44/4.41 tff(252,plain,
% 6.44/4.41 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0)))))),
% 6.44/4.41 inference(monotonicity,[status(thm)],[251])).
% 6.44/4.41 tff(253,plain,
% 6.44/4.41 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.44/4.41 inference(transitivity,[status(thm)],[252, 250])).
% 6.44/4.41 tff(254,plain,
% 6.44/4.41 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 6.44/4.41 inference(quant_inst,[status(thm)],[])).
% 6.44/4.41 tff(255,plain,
% 6.44/4.41 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(tptp_fun_D_11(k6_lattices(A!0), A!0, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.44/4.42 inference(modus_ponens,[status(thm)],[254, 253])).
% 6.44/4.42 tff(256,plain,
% 6.44/4.42 (r3_lattices(A!0, B!1, B!1)),
% 6.44/4.42 inference(unit_resolution,[status(thm)],[255, 37, 35, 34, 249, 236, 234, 232, 210])).
% 6.44/4.42 tff(257,plain,
% 6.44/4.42 ((~(r2_hidden(B!1, k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, B!1))) | r2_hidden(B!1, k2_filter_0(A!0, B!1)) | (~r3_lattices(A!0, B!1, B!1))),
% 6.44/4.42 inference(tautology,[status(thm)],[])).
% 6.44/4.42 tff(258,plain,
% 6.44/4.42 (r2_hidden(B!1, k2_filter_0(A!0, B!1))),
% 6.44/4.42 inference(unit_resolution,[status(thm)],[257, 256, 110])).
% 6.44/4.42 tff(259,plain,
% 6.44/4.42 (r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))),
% 6.44/4.42 inference(modus_ponens,[status(thm)],[258, 79])).
% 6.44/4.42 tff(260,plain,
% 6.44/4.42 ((~((~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))))) | (~r2_hidden(B!1, a_2_0_filter_0(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1)))))),
% 6.44/4.42 inference(tautology,[status(thm)],[])).
% 6.44/4.42 tff(261,plain,
% 6.44/4.42 (~((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1))))),
% 6.44/4.42 inference(unit_resolution,[status(thm)],[260, 259, 49])).
% 6.44/4.42 tff(262,plain,
% 6.44/4.42 (((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1)))) | (B!1 = tptp_fun_D_11(B!1, A!0, B!1))),
% 6.44/4.42 inference(tautology,[status(thm)],[])).
% 6.44/4.42 tff(263,plain,
% 6.44/4.42 (B!1 = tptp_fun_D_11(B!1, A!0, B!1)),
% 6.44/4.42 inference(unit_resolution,[status(thm)],[262, 261])).
% 6.44/4.42 tff(264,plain,
% 6.44/4.42 (tptp_fun_D_11(B!1, A!0, B!1) = B!1),
% 6.44/4.42 inference(symmetry,[status(thm)],[263])).
% 6.44/4.42 tff(265,plain,
% 6.44/4.42 (r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.44/4.42 inference(monotonicity,[status(thm)],[264])).
% 6.44/4.42 tff(266,plain,
% 6.44/4.42 (r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.44/4.42 inference(symmetry,[status(thm)],[265])).
% 6.44/4.42 tff(267,plain,
% 6.44/4.42 ((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) <=> (~r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.44/4.42 inference(monotonicity,[status(thm)],[266])).
% 6.44/4.42 tff(268,assumption,(~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))), introduced(assumption)).
% 6.44/4.42 tff(269,plain,
% 6.44/4.42 (~r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.44/4.42 inference(modus_ponens,[status(thm)],[268, 267])).
% 6.44/4.42 tff(270,plain,
% 6.44/4.42 (k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1)) = k2_filter_0(A!0, B!1)),
% 6.44/4.42 inference(monotonicity,[status(thm)],[264])).
% 6.44/4.42 tff(271,plain,
% 6.44/4.42 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 6.44/4.42 inference(monotonicity,[status(thm)],[270])).
% 6.44/4.42 tff(272,plain,
% 6.44/4.42 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1)))),
% 6.44/4.42 inference(symmetry,[status(thm)],[271])).
% 6.44/4.42 tff(273,plain,
% 6.44/4.42 (((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))) | r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.44/4.42 inference(tautology,[status(thm)],[])).
% 6.44/4.42 tff(274,plain,
% 6.44/4.42 ((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 6.44/4.42 inference(unit_resolution,[status(thm)],[273, 268])).
% 6.44/4.42 tff(275,plain,
% 6.44/4.42 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 6.44/4.42 inference(bind,[status(th)],[])).
% 6.44/4.42 tff(276,plain,
% 6.44/4.42 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(quant_intro,[status(thm)],[275])).
% 6.44/4.42 tff(277,plain,
% 6.44/4.42 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(rewrite,[status(thm)],[])).
% 6.44/4.42 tff(278,plain,
% 6.44/4.42 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 6.44/4.42 inference(bind,[status(th)],[])).
% 6.44/4.42 tff(279,plain,
% 6.44/4.42 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(quant_intro,[status(thm)],[278])).
% 6.44/4.42 tff(280,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 6.44/4.42 tff(281,plain,
% 6.44/4.42 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(modus_ponens,[status(thm)],[280, 279])).
% 6.44/4.42 tff(282,plain,
% 6.44/4.42 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(modus_ponens,[status(thm)],[281, 277])).
% 6.44/4.42 tff(283,plain,(
% 6.44/4.42 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(skolemize,[status(sab)],[282])).
% 6.44/4.42 tff(284,plain,
% 6.44/4.42 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 6.44/4.42 inference(modus_ponens,[status(thm)],[283, 276])).
% 6.44/4.42 tff(285,plain,
% 6.44/4.42 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 6.44/4.42 inference(rewrite,[status(thm)],[])).
% 6.44/4.42 tff(286,plain,
% 6.44/4.42 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 6.44/4.42 inference(quant_inst,[status(thm)],[])).
% 6.44/4.42 tff(287,plain,
% 6.46/4.42 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[286, 285])).
% 6.46/4.42 tff(288,plain,
% 6.46/4.42 (l1_struct_0(A!0)),
% 6.46/4.42 inference(unit_resolution,[status(thm)],[287, 284, 129])).
% 6.46/4.42 tff(289,plain,
% 6.46/4.42 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(290,plain,
% 6.46/4.42 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[289])).
% 6.46/4.42 tff(291,plain,
% 6.46/4.42 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(292,plain,
% 6.46/4.42 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[291])).
% 6.46/4.42 tff(293,plain,
% 6.46/4.42 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(294,plain,
% 6.46/4.42 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(295,plain,
% 6.46/4.42 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[294])).
% 6.46/4.42 tff(296,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 6.46/4.42 tff(297,plain,
% 6.46/4.42 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[296, 295])).
% 6.46/4.42 tff(298,plain,
% 6.46/4.42 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[297, 293])).
% 6.46/4.42 tff(299,plain,(
% 6.46/4.42 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 6.46/4.42 inference(skolemize,[status(sab)],[298])).
% 6.46/4.42 tff(300,plain,
% 6.46/4.42 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[299, 292])).
% 6.46/4.42 tff(301,plain,
% 6.46/4.42 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[300, 290])).
% 6.46/4.42 tff(302,plain,
% 6.46/4.42 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(303,plain,
% 6.46/4.42 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(304,plain,
% 6.46/4.42 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 6.46/4.42 inference(monotonicity,[status(thm)],[303])).
% 6.46/4.42 tff(305,plain,
% 6.46/4.42 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 6.46/4.42 inference(transitivity,[status(thm)],[304, 302])).
% 6.46/4.42 tff(306,plain,
% 6.46/4.42 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 6.46/4.42 inference(quant_inst,[status(thm)],[])).
% 6.46/4.42 tff(307,plain,
% 6.46/4.42 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[306, 305])).
% 6.46/4.42 tff(308,plain,
% 6.46/4.42 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 6.46/4.42 inference(unit_resolution,[status(thm)],[307, 37, 301])).
% 6.46/4.42 tff(309,plain,
% 6.46/4.42 (~v1_xboole_0(u1_struct_0(A!0))),
% 6.46/4.42 inference(unit_resolution,[status(thm)],[308, 288])).
% 6.46/4.42 tff(310,plain,
% 6.46/4.42 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(311,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[310])).
% 6.46/4.42 tff(312,plain,
% 6.46/4.42 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(313,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[312])).
% 6.46/4.42 tff(314,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 6.46/4.42 inference(transitivity,[status(thm)],[313, 311])).
% 6.46/4.42 tff(315,plain,
% 6.46/4.42 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(316,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[315])).
% 6.46/4.42 tff(317,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(318,plain,
% 6.46/4.42 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))) <=> (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(319,plain,
% 6.46/4.42 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[318])).
% 6.46/4.42 tff(320,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_filter_2')).
% 6.46/4.42 tff(321,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[320, 319])).
% 6.46/4.42 tff(322,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[321, 317])).
% 6.46/4.42 tff(323,plain,(
% 6.46/4.42 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))),
% 6.46/4.42 inference(skolemize,[status(sab)],[322])).
% 6.46/4.42 tff(324,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[323, 316])).
% 6.46/4.42 tff(325,plain,
% 6.46/4.42 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[324, 314])).
% 6.46/4.42 tff(326,plain,
% 6.46/4.42 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(327,plain,
% 6.46/4.42 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 6.46/4.42 inference(quant_inst,[status(thm)],[])).
% 6.46/4.42 tff(328,plain,
% 6.46/4.42 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[327, 326])).
% 6.46/4.42 tff(329,plain,
% 6.46/4.42 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 6.46/4.42 inference(unit_resolution,[status(thm)],[328, 325, 309])).
% 6.46/4.42 tff(330,plain,
% 6.46/4.42 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(331,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[330])).
% 6.46/4.42 tff(332,plain,
% 6.46/4.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), rewrite(((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)) <=> (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(333,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[332])).
% 6.46/4.42 tff(334,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(335,plain,
% 6.46/4.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 6.46/4.42 inference(bind,[status(th)],[])).
% 6.46/4.42 tff(336,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 6.46/4.42 inference(quant_intro,[status(thm)],[335])).
% 6.46/4.42 tff(337,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k22_filter_2')).
% 6.46/4.42 tff(338,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[337, 336])).
% 6.46/4.42 tff(339,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[338, 334])).
% 6.46/4.42 tff(340,plain,(
% 6.46/4.42 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 6.46/4.42 inference(skolemize,[status(sab)],[339])).
% 6.46/4.42 tff(341,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[340, 333])).
% 6.46/4.42 tff(342,plain,
% 6.46/4.42 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 6.46/4.42 inference(modus_ponens,[status(thm)],[341, 331])).
% 6.46/4.42 tff(343,plain,
% 6.46/4.42 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(344,plain,
% 6.46/4.42 ((v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 6.46/4.42 inference(rewrite,[status(thm)],[])).
% 6.46/4.42 tff(345,plain,
% 6.46/4.42 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))))),
% 6.46/4.42 inference(monotonicity,[status(thm)],[344])).
% 6.46/4.42 tff(346,plain,
% 6.46/4.42 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 6.46/4.43 inference(transitivity,[status(thm)],[345, 343])).
% 6.46/4.43 tff(347,plain,
% 6.46/4.43 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 6.46/4.43 inference(quant_inst,[status(thm)],[])).
% 6.46/4.43 tff(348,plain,
% 6.46/4.43 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[347, 346])).
% 6.46/4.43 tff(349,plain,
% 6.46/4.43 ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[348, 37, 36, 35, 34, 342])).
% 6.46/4.43 tff(350,plain,
% 6.46/4.43 (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[349, 147])).
% 6.46/4.43 tff(351,plain,
% 6.46/4.43 ((v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))) | m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)),
% 6.46/4.43 inference(tautology,[status(thm)],[])).
% 6.46/4.43 tff(352,plain,
% 6.46/4.43 (m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[351, 350])).
% 6.46/4.43 tff(353,plain,
% 6.46/4.43 (^[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))))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(354,plain,
% 6.46/4.43 (![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)))))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[353])).
% 6.46/4.43 tff(355,plain,
% 6.46/4.43 (^[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))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(356,plain,
% 6.46/4.43 (![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)))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[355])).
% 6.46/4.43 tff(357,plain,
% 6.46/4.43 (^[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))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(358,plain,
% 6.46/4.43 (![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)))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[357])).
% 6.46/4.43 tff(359,plain,
% 6.46/4.43 (![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)))),
% 6.46/4.43 inference(transitivity,[status(thm)],[358, 356])).
% 6.46/4.43 tff(360,plain,
% 6.46/4.43 (^[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)))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(361,plain,
% 6.46/4.43 (![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)))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[360])).
% 6.46/4.43 tff(362,plain,
% 6.46/4.43 (![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)))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(363,plain,
% 6.46/4.43 (^[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)))))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(364,plain,
% 6.46/4.43 (![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)))))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[363])).
% 6.46/4.43 tff(365,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')).
% 6.46/4.43 tff(366,plain,
% 6.46/4.43 (![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)))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[365, 364])).
% 6.46/4.43 tff(367,plain,
% 6.46/4.43 (![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)))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[366, 362])).
% 6.46/4.43 tff(368,plain,(
% 6.46/4.43 ![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)))))),
% 6.46/4.43 inference(skolemize,[status(sab)],[367])).
% 6.46/4.43 tff(369,plain,
% 6.46/4.43 (![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)))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[368, 361])).
% 6.46/4.43 tff(370,plain,
% 6.46/4.43 (![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)))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[369, 359])).
% 6.46/4.43 tff(371,plain,
% 6.46/4.43 (![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)))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[370, 354])).
% 6.46/4.43 tff(372,plain,
% 6.46/4.43 (((~![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)))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(373,plain,
% 6.46/4.43 ((~![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)))))),
% 6.46/4.43 inference(quant_inst,[status(thm)],[])).
% 6.46/4.43 tff(374,plain,
% 6.46/4.43 ((~![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))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[373, 372])).
% 6.46/4.43 tff(375,plain,
% 6.46/4.43 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[374, 37, 36, 35, 371])).
% 6.46/4.43 tff(376,plain,
% 6.46/4.43 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(377,plain,
% 6.46/4.43 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 6.46/4.43 inference(quant_inst,[status(thm)],[])).
% 6.46/4.43 tff(378,plain,
% 6.46/4.43 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[377, 376])).
% 6.46/4.43 tff(379,plain,
% 6.46/4.43 (m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[378, 375, 352])).
% 6.46/4.43 tff(380,plain,
% 6.46/4.43 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C))))))))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(381,plain,
% 6.46/4.43 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C))))))))))),
% 6.46/4.43 inference(quant_inst,[status(thm)],[])).
% 6.46/4.43 tff(382,plain,
% 6.46/4.43 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C)))))))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[381, 380])).
% 6.46/4.43 tff(383,plain,
% 6.46/4.43 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C)))))))))),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[382, 379, 329])).
% 6.46/4.43 tff(384,plain,
% 6.46/4.43 (^[A: $i, B: $i] : refl((m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(385,plain,
% 6.46/4.43 (![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[384])).
% 6.46/4.43 tff(386,plain,
% 6.46/4.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_0(k2_filter_0(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_0(k2_filter_0(A, B), A)) <=> (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(387,plain,
% 6.46/4.43 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> ![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[386])).
% 6.46/4.43 tff(388,plain,
% 6.46/4.43 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(389,plain,
% 6.46/4.43 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(390,plain,
% 6.46/4.43 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[389])).
% 6.46/4.43 tff(391,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_filter_0')).
% 6.46/4.43 tff(392,plain,
% 6.46/4.43 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[391, 390])).
% 6.46/4.43 tff(393,plain,
% 6.46/4.43 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[392, 388])).
% 6.46/4.43 tff(394,plain,(
% 6.46/4.43 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 6.46/4.43 inference(skolemize,[status(sab)],[393])).
% 6.46/4.43 tff(395,plain,
% 6.46/4.43 (![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[394, 387])).
% 6.46/4.43 tff(396,plain,
% 6.46/4.43 (![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[395, 385])).
% 6.46/4.43 tff(397,plain,
% 6.46/4.43 (((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))) <=> ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(398,plain,
% 6.46/4.43 ((m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(399,plain,
% 6.46/4.43 (((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0)))),
% 6.46/4.43 inference(monotonicity,[status(thm)],[398])).
% 6.46/4.43 tff(400,plain,
% 6.46/4.43 (((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))),
% 6.46/4.43 inference(transitivity,[status(thm)],[399, 397])).
% 6.46/4.43 tff(401,plain,
% 6.46/4.43 ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 6.46/4.43 inference(quant_inst,[status(thm)],[])).
% 6.46/4.43 tff(402,plain,
% 6.46/4.43 ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0)),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[401, 400])).
% 6.46/4.43 tff(403,plain,
% 6.46/4.43 (m1_filter_0(k2_filter_0(A!0, B!1), A!0)),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[402, 37, 36, 35, 34, 396])).
% 6.46/4.43 tff(404,plain,
% 6.46/4.43 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(405,plain,
% 6.46/4.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[404])).
% 6.46/4.43 tff(406,plain,
% 6.46/4.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(407,plain,
% 6.46/4.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[406])).
% 6.46/4.43 tff(408,plain,
% 6.46/4.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(transitivity,[status(thm)],[407, 405])).
% 6.46/4.43 tff(409,plain,
% 6.46/4.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(410,plain,
% 6.46/4.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[409])).
% 6.46/4.43 tff(411,plain,
% 6.46/4.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(412,plain,
% 6.46/4.43 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(bind,[status(th)],[])).
% 6.46/4.43 tff(413,plain,
% 6.46/4.43 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 6.46/4.43 inference(quant_intro,[status(thm)],[412])).
% 6.46/4.43 tff(414,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 6.46/4.43 tff(415,plain,
% 6.46/4.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[414, 413])).
% 6.46/4.43 tff(416,plain,
% 6.46/4.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[415, 411])).
% 6.46/4.43 tff(417,plain,(
% 6.46/4.43 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 6.46/4.43 inference(skolemize,[status(sab)],[416])).
% 6.46/4.43 tff(418,plain,
% 6.46/4.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[417, 410])).
% 6.46/4.43 tff(419,plain,
% 6.46/4.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[418, 408])).
% 6.46/4.43 tff(420,plain,
% 6.46/4.43 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(421,plain,
% 6.46/4.43 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 6.46/4.43 inference(quant_inst,[status(thm)],[])).
% 6.46/4.43 tff(422,plain,
% 6.46/4.43 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 6.46/4.43 inference(modus_ponens,[status(thm)],[421, 420])).
% 6.46/4.43 tff(423,plain,
% 6.46/4.43 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 6.46/4.43 inference(unit_resolution,[status(thm)],[422, 37, 36, 35, 419])).
% 6.46/4.43 tff(424,plain,
% 6.46/4.43 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 6.46/4.43 inference(rewrite,[status(thm)],[])).
% 6.46/4.43 tff(425,plain,
% 6.46/4.43 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 6.46/4.44 inference(quant_inst,[status(thm)],[])).
% 6.46/4.44 tff(426,plain,
% 6.46/4.44 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[425, 424])).
% 6.46/4.44 tff(427,plain,
% 6.46/4.44 (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[426, 423, 403])).
% 6.46/4.44 tff(428,plain,
% 6.46/4.44 ((v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))) | m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 6.46/4.44 inference(tautology,[status(thm)],[])).
% 6.46/4.44 tff(429,plain,
% 6.46/4.44 (m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[428, 427])).
% 6.46/4.44 tff(430,plain,
% 6.46/4.44 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, k2_filter_0(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, k2_filter_0(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))))))))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(431,plain,
% 6.46/4.44 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, k2_filter_0(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))))))))),
% 6.46/4.44 inference(quant_inst,[status(thm)],[])).
% 6.46/4.44 tff(432,plain,
% 6.46/4.44 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, k2_filter_0(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))))))))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[431, 430])).
% 6.46/4.44 tff(433,plain,
% 6.46/4.44 (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, k2_filter_0(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))))))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[432, 429, 383])).
% 6.46/4.44 tff(434,plain,
% 6.46/4.44 (((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(D, k2_filter_0(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))))))) | (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))))),
% 6.46/4.44 inference(tautology,[status(thm)],[])).
% 6.46/4.44 tff(435,plain,
% 6.46/4.44 (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[434, 433])).
% 6.46/4.44 tff(436,plain,
% 6.46/4.44 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 6.46/4.44 inference(bind,[status(th)],[])).
% 6.46/4.44 tff(437,plain,
% 6.46/4.44 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.44 inference(quant_intro,[status(thm)],[436])).
% 6.46/4.44 tff(438,plain,
% 6.46/4.44 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 6.46/4.44 inference(bind,[status(th)],[])).
% 6.46/4.44 tff(439,plain,
% 6.46/4.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.44 inference(quant_intro,[status(thm)],[438])).
% 6.46/4.44 tff(440,plain,
% 6.46/4.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(441,plain,
% 6.46/4.44 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 6.46/4.44 inference(bind,[status(th)],[])).
% 6.46/4.44 tff(442,plain,
% 6.46/4.44 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 6.46/4.44 inference(quant_intro,[status(thm)],[441])).
% 6.46/4.44 tff(443,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 6.46/4.44 tff(444,plain,
% 6.46/4.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[443, 442])).
% 6.46/4.44 tff(445,plain,
% 6.46/4.44 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[444, 440])).
% 6.46/4.44 tff(446,plain,(
% 6.46/4.44 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 6.46/4.44 inference(skolemize,[status(sab)],[445])).
% 6.46/4.44 tff(447,plain,
% 6.46/4.44 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[446, 439])).
% 6.46/4.44 tff(448,plain,
% 6.46/4.44 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[447, 437])).
% 6.46/4.44 tff(449,plain,
% 6.46/4.44 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(450,plain,
% 6.46/4.44 ((v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(451,plain,
% 6.46/4.44 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1))))),
% 6.46/4.44 inference(monotonicity,[status(thm)],[450])).
% 6.46/4.44 tff(452,plain,
% 6.46/4.44 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))),
% 6.46/4.44 inference(transitivity,[status(thm)],[451, 449])).
% 6.46/4.44 tff(453,plain,
% 6.46/4.44 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 6.46/4.44 inference(quant_inst,[status(thm)],[])).
% 6.46/4.44 tff(454,plain,
% 6.46/4.44 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[453, 452])).
% 6.46/4.44 tff(455,plain,
% 6.46/4.44 (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[454, 37, 36, 35, 34, 448])).
% 6.46/4.44 tff(456,plain,
% 6.46/4.44 (k2_filter_0(A!0, B!1) = k2_filter_2(A!0, B!1)),
% 6.46/4.44 inference(symmetry,[status(thm)],[455])).
% 6.46/4.44 tff(457,plain,
% 6.46/4.44 (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) <=> r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))),
% 6.46/4.44 inference(monotonicity,[status(thm)],[456])).
% 6.46/4.44 tff(458,plain,
% 6.46/4.44 (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1)) <=> r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))),
% 6.46/4.44 inference(symmetry,[status(thm)],[457])).
% 6.46/4.44 tff(459,plain,
% 6.46/4.44 ((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) <=> (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)))),
% 6.46/4.44 inference(monotonicity,[status(thm)],[458])).
% 6.46/4.44 tff(460,plain,
% 6.46/4.44 (m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 6.46/4.44 inference(monotonicity,[status(thm)],[456])).
% 6.46/4.44 tff(461,plain,
% 6.46/4.44 (m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[429, 460])).
% 6.46/4.44 tff(462,plain,
% 6.46/4.44 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 6.46/4.44 inference(bind,[status(th)],[])).
% 6.46/4.44 tff(463,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 6.46/4.44 inference(quant_intro,[status(thm)],[462])).
% 6.46/4.44 tff(464,plain,
% 6.46/4.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))))), rewrite((r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 6.46/4.44 inference(bind,[status(th)],[])).
% 6.46/4.44 tff(465,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 6.46/4.44 inference(quant_intro,[status(thm)],[464])).
% 6.46/4.44 tff(466,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(467,plain,
% 6.46/4.44 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), rewrite((r1_filter_2(A, B, C) => r1_filter_2(A, C, B)) <=> ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))))),
% 6.46/4.44 inference(bind,[status(th)],[])).
% 6.46/4.44 tff(468,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 6.46/4.44 inference(quant_intro,[status(thm)],[467])).
% 6.46/4.44 tff(469,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_filter_2')).
% 6.46/4.44 tff(470,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[469, 468])).
% 6.46/4.44 tff(471,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[470, 466])).
% 6.46/4.44 tff(472,plain,(
% 6.46/4.44 ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 6.46/4.44 inference(skolemize,[status(sab)],[471])).
% 6.46/4.44 tff(473,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[472, 465])).
% 6.46/4.44 tff(474,plain,
% 6.46/4.44 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[473, 463])).
% 6.46/4.44 tff(475,plain,
% 6.46/4.44 (~r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 6.46/4.44 inference(or_elim,[status(thm)],[33])).
% 6.46/4.44 tff(476,plain,
% 6.46/4.44 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(477,plain,
% 6.46/4.44 ((v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 6.46/4.44 inference(rewrite,[status(thm)],[])).
% 6.46/4.44 tff(478,plain,
% 6.46/4.44 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 6.46/4.44 inference(monotonicity,[status(thm)],[477])).
% 6.46/4.44 tff(479,plain,
% 6.46/4.44 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 6.46/4.44 inference(transitivity,[status(thm)],[478, 476])).
% 6.46/4.44 tff(480,plain,
% 6.46/4.44 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 6.46/4.44 inference(quant_inst,[status(thm)],[])).
% 6.46/4.44 tff(481,plain,
% 6.46/4.44 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[480, 479])).
% 6.46/4.44 tff(482,plain,
% 6.46/4.44 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k2_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[481, 475, 474])).
% 6.46/4.44 tff(483,plain,
% 6.46/4.44 (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_2(A!0, B!1))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[482, 461, 309, 379])).
% 6.46/4.44 tff(484,plain,
% 6.46/4.44 (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1))),
% 6.46/4.44 inference(modus_ponens,[status(thm)],[483, 459])).
% 6.46/4.44 tff(485,plain,
% 6.46/4.44 ((~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))))) | r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))))),
% 6.46/4.44 inference(tautology,[status(thm)],[])).
% 6.46/4.44 tff(486,plain,
% 6.46/4.44 (~((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))),
% 6.46/4.44 inference(unit_resolution,[status(thm)],[485, 484, 435])).
% 6.46/4.44 tff(487,plain,
% 6.46/4.44 (((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))) | m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 6.46/4.45 inference(tautology,[status(thm)],[])).
% 6.46/4.45 tff(488,plain,
% 6.46/4.45 (m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 6.46/4.45 inference(unit_resolution,[status(thm)],[487, 486])).
% 6.46/4.45 tff(489,plain,
% 6.46/4.45 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))))),
% 6.46/4.45 inference(bind,[status(th)],[])).
% 6.46/4.45 tff(490,plain,
% 6.46/4.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 6.46/4.45 inference(quant_intro,[status(thm)],[489])).
% 6.46/4.45 tff(491,plain,
% 6.46/4.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))))),
% 6.46/4.45 inference(bind,[status(th)],[])).
% 6.46/4.45 tff(492,plain,
% 6.46/4.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 6.46/4.45 inference(quant_intro,[status(thm)],[491])).
% 6.46/4.45 tff(493,plain,
% 6.46/4.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 6.46/4.45 inference(transitivity,[status(thm)],[492, 490])).
% 6.46/4.45 tff(494,plain,
% 6.46/4.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))))),
% 6.46/4.45 inference(bind,[status(th)],[])).
% 6.46/4.45 tff(495,plain,
% 6.46/4.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 6.46/4.45 inference(quant_intro,[status(thm)],[494])).
% 6.46/4.45 tff(496,plain,
% 6.46/4.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(497,plain,
% 6.46/4.45 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))) <=> ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))))),
% 6.46/4.45 inference(bind,[status(th)],[])).
% 6.46/4.45 tff(498,plain,
% 6.46/4.45 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 6.46/4.45 inference(quant_intro,[status(thm)],[497])).
% 6.46/4.45 tff(499,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_filter_2')).
% 6.46/4.45 tff(500,plain,
% 6.46/4.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[499, 498])).
% 6.46/4.45 tff(501,plain,
% 6.46/4.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[500, 496])).
% 6.46/4.45 tff(502,plain,(
% 6.46/4.45 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 6.46/4.45 inference(skolemize,[status(sab)],[501])).
% 6.46/4.45 tff(503,plain,
% 6.46/4.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[502, 495])).
% 6.46/4.45 tff(504,plain,
% 6.46/4.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[503, 493])).
% 6.46/4.45 tff(505,plain,
% 6.46/4.45 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C)))))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(506,plain,
% 6.46/4.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C)))))))))),
% 6.46/4.45 inference(quant_inst,[status(thm)],[])).
% 6.46/4.45 tff(507,plain,
% 6.46/4.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[506, 505])).
% 6.46/4.45 tff(508,plain,
% 6.46/4.45 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))),
% 6.46/4.45 inference(unit_resolution,[status(thm)],[507, 37, 36, 35, 504])).
% 6.46/4.45 tff(509,plain,
% 6.46/4.45 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(510,plain,
% 6.46/4.45 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))))))))),
% 6.46/4.45 inference(quant_inst,[status(thm)],[])).
% 6.46/4.45 tff(511,plain,
% 6.46/4.45 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[510, 509])).
% 6.46/4.45 tff(512,plain,
% 6.46/4.45 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))),
% 6.46/4.45 inference(unit_resolution,[status(thm)],[511, 34, 508])).
% 6.46/4.45 tff(513,plain,
% 6.46/4.45 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(514,plain,
% 6.46/4.45 (((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) <=> ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(515,plain,
% 6.46/4.45 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))))),
% 6.46/4.45 inference(monotonicity,[status(thm)],[514])).
% 6.46/4.45 tff(516,plain,
% 6.46/4.45 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))),
% 6.46/4.45 inference(transitivity,[status(thm)],[515, 513])).
% 6.46/4.45 tff(517,plain,
% 6.46/4.45 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0))))))))),
% 6.46/4.45 inference(quant_inst,[status(thm)],[])).
% 6.46/4.45 tff(518,plain,
% 6.46/4.45 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, C)) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C)))))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[517, 516])).
% 6.46/4.45 tff(519,plain,
% 6.46/4.45 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))),
% 6.46/4.45 inference(unit_resolution,[status(thm)],[518, 147, 512])).
% 6.46/4.45 tff(520,plain,
% 6.46/4.45 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0)))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(521,plain,
% 6.46/4.45 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0)))),
% 6.46/4.45 inference(quant_inst,[status(thm)],[])).
% 6.46/4.45 tff(522,plain,
% 6.46/4.45 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0))),
% 6.46/4.45 inference(modus_ponens,[status(thm)],[521, 520])).
% 6.46/4.45 tff(523,plain,
% 6.46/4.45 (r3_lattices(A!0, B!1, k6_lattices(A!0))),
% 6.46/4.45 inference(unit_resolution,[status(thm)],[522, 34, 198])).
% 6.46/4.45 tff(524,plain,
% 6.46/4.45 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(525,plain,
% 6.46/4.45 (((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))))) <=> ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))),
% 6.46/4.45 inference(rewrite,[status(thm)],[])).
% 6.46/4.45 tff(526,plain,
% 6.46/4.45 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))))))),
% 6.46/4.46 inference(monotonicity,[status(thm)],[525])).
% 6.46/4.46 tff(527,plain,
% 6.46/4.46 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))),
% 6.46/4.46 inference(transitivity,[status(thm)],[526, 524])).
% 6.46/4.46 tff(528,plain,
% 6.46/4.46 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))))),
% 6.46/4.46 inference(quant_inst,[status(thm)],[])).
% 6.46/4.46 tff(529,plain,
% 6.46/4.46 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))))))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[528, 527])).
% 6.46/4.46 tff(530,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[529, 523, 519, 488])).
% 6.46/4.46 tff(531,plain,
% 6.46/4.46 ((~(r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))))) | (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(532,plain,
% 6.46/4.46 ((~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[531, 530])).
% 6.46/4.46 tff(533,plain,
% 6.46/4.46 (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[532, 274])).
% 6.46/4.46 tff(534,plain,
% 6.46/4.46 (((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))) | (~(r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(535,plain,
% 6.46/4.46 (~(r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[534, 486])).
% 6.46/4.46 tff(536,plain,
% 6.46/4.46 ((r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) | r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(537,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[536, 535])).
% 6.46/4.46 tff(538,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[537, 533])).
% 6.46/4.46 tff(539,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1)))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[538, 272])).
% 6.46/4.46 tff(540,plain,
% 6.46/4.46 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))))),
% 6.46/4.46 inference(rewrite,[status(thm)],[])).
% 6.46/4.46 tff(541,plain,
% 6.46/4.46 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))))),
% 6.46/4.46 inference(quant_inst,[status(thm)],[])).
% 6.46/4.46 tff(542,plain,
% 6.46/4.46 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[541, 540])).
% 6.46/4.46 tff(543,plain,
% 6.46/4.46 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[542, 102, 488])).
% 6.46/4.46 tff(544,plain,
% 6.46/4.46 (((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, B!1, tptp_fun_D_11(B!1, A!0, B!1)))) | m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(545,plain,
% 6.46/4.46 (m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[544, 261])).
% 6.46/4.46 tff(546,plain,
% 6.46/4.46 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))) | ((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))) | (~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))),
% 6.46/4.46 inference(rewrite,[status(thm)],[])).
% 6.46/4.46 tff(547,plain,
% 6.46/4.46 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))) | ((~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))),
% 6.46/4.46 inference(quant_inst,[status(thm)],[])).
% 6.46/4.46 tff(548,plain,
% 6.46/4.46 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))))) | (~m1_subset_1(tptp_fun_D_11(B!1, A!0, B!1), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[547, 546])).
% 6.46/4.46 tff(549,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[548, 545, 543])).
% 6.46/4.46 tff(550,plain,
% 6.46/4.46 ((~(r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))) | (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1)))) | r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(551,plain,
% 6.46/4.46 ((~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1)))) | r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[550, 549])).
% 6.46/4.46 tff(552,plain,
% 6.46/4.46 ($false),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[551, 539, 269])).
% 6.46/4.46 tff(553,plain,(r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))), inference(lemma,lemma(discharge,[]))).
% 6.46/4.46 tff(554,plain,
% 6.46/4.46 (r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[553, 266])).
% 6.46/4.46 tff(555,plain,
% 6.46/4.46 ((~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) <=> (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))))),
% 6.46/4.46 inference(monotonicity,[status(thm)],[272])).
% 6.46/4.46 tff(556,plain,
% 6.46/4.46 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 6.46/4.46 inference(rewrite,[status(thm)],[])).
% 6.46/4.46 tff(557,plain,
% 6.46/4.46 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 6.46/4.46 inference(quant_inst,[status(thm)],[])).
% 6.46/4.46 tff(558,plain,
% 6.46/4.46 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[557, 556])).
% 6.46/4.46 tff(559,plain,
% 6.46/4.46 (r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[558, 198, 488])).
% 6.46/4.46 tff(560,plain,
% 6.46/4.46 ((~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))) | (~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(561,plain,
% 6.46/4.46 ((~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))) | (~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[560, 559])).
% 6.46/4.46 tff(562,plain,
% 6.46/4.46 (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[561, 553])).
% 6.46/4.46 tff(563,plain,
% 6.46/4.46 ((~(r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))))) | r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | ((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(564,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | ((~r3_lattices(A!0, B!1, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k6_lattices(A!0))))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[563, 530])).
% 6.46/4.46 tff(565,plain,
% 6.46/4.46 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[564, 562])).
% 6.46/4.46 tff(566,plain,
% 6.46/4.46 ((r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) | (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))),
% 6.46/4.46 inference(tautology,[status(thm)],[])).
% 6.46/4.46 tff(567,plain,
% 6.46/4.46 ((~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[566, 535])).
% 6.46/4.46 tff(568,plain,
% 6.46/4.46 (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 6.46/4.46 inference(unit_resolution,[status(thm)],[567, 565])).
% 6.46/4.46 tff(569,plain,
% 6.46/4.46 (~r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1)))),
% 6.46/4.46 inference(modus_ponens,[status(thm)],[568, 555])).
% 6.46/4.46 tff(570,plain,
% 6.46/4.46 ((~(r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) <=> r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))) | r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.46/4.48 inference(tautology,[status(thm)],[])).
% 6.46/4.48 tff(571,plain,
% 6.46/4.48 (r2_hidden(tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0)), k2_filter_0(A!0, tptp_fun_D_11(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_11(B!1, A!0, B!1), tptp_fun_D_2(k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)), u1_struct_0(A!0))))),
% 6.46/4.48 inference(unit_resolution,[status(thm)],[570, 549])).
% 6.46/4.48 tff(572,plain,
% 6.46/4.48 ($false),
% 6.46/4.48 inference(unit_resolution,[status(thm)],[571, 569, 554])).
% 6.46/4.48 % SZS output end Proof
%------------------------------------------------------------------------------