TSTP Solution File: LAT305+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT305+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:53 EDT 2022
% Result : Theorem 160.68s 103.17s
% Output : Proof 160.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LAT305+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 13:57:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 160.68/103.17 % SZS status Theorem
% 160.68/103.17 % SZS output start Proof
% 160.68/103.17 tff(m1_subset_1_type, type, (
% 160.68/103.17 m1_subset_1: ( $i * $i ) > $o)).
% 160.68/103.17 tff(u1_struct_0_type, type, (
% 160.68/103.17 u1_struct_0: $i > $i)).
% 160.68/103.17 tff(tptp_fun_A_0_type, type, (
% 160.68/103.17 tptp_fun_A_0: $i)).
% 160.68/103.17 tff(k2_binop_1_type, type, (
% 160.68/103.17 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 160.68/103.17 tff(tptp_fun_B_1_type, type, (
% 160.68/103.17 tptp_fun_B_1: $i)).
% 160.68/103.17 tff(tptp_fun_C_2_type, type, (
% 160.68/103.17 tptp_fun_C_2: $i)).
% 160.68/103.17 tff(u1_lattices_type, type, (
% 160.68/103.17 u1_lattices: $i > $i)).
% 160.68/103.17 tff(r3_lattices_type, type, (
% 160.68/103.17 r3_lattices: ( $i * $i * $i ) > $o)).
% 160.68/103.17 tff(r2_hidden_type, type, (
% 160.68/103.17 r2_hidden: ( $i * $i ) > $o)).
% 160.68/103.17 tff(a_2_0_filter_2_type, type, (
% 160.68/103.17 a_2_0_filter_2: ( $i * $i ) > $i)).
% 160.68/103.17 tff(tptp_fun_D_12_type, type, (
% 160.68/103.17 tptp_fun_D_12: ( $i * $i * $i ) > $i)).
% 160.68/103.17 tff(l3_lattices_type, type, (
% 160.68/103.17 l3_lattices: $i > $o)).
% 160.68/103.17 tff(v10_lattices_type, type, (
% 160.68/103.17 v10_lattices: $i > $o)).
% 160.68/103.17 tff(v3_struct_0_type, type, (
% 160.68/103.17 v3_struct_0: $i > $o)).
% 160.68/103.17 tff(k18_filter_2_type, type, (
% 160.68/103.17 k18_filter_2: ( $i * $i ) > $i)).
% 160.68/103.17 tff(k4_lattices_type, type, (
% 160.68/103.17 k4_lattices: ( $i * $i * $i ) > $i)).
% 160.68/103.17 tff(k2_lattices_type, type, (
% 160.68/103.17 k2_lattices: ( $i * $i * $i ) > $i)).
% 160.68/103.17 tff(l1_lattices_type, type, (
% 160.68/103.17 l1_lattices: $i > $o)).
% 160.68/103.17 tff(l2_lattices_type, type, (
% 160.68/103.17 l2_lattices: $i > $o)).
% 160.68/103.17 tff(v6_lattices_type, type, (
% 160.68/103.17 v6_lattices: $i > $o)).
% 160.68/103.17 tff(v9_lattices_type, type, (
% 160.68/103.17 v9_lattices: $i > $o)).
% 160.68/103.17 tff(v8_lattices_type, type, (
% 160.68/103.17 v8_lattices: $i > $o)).
% 160.68/103.17 tff(v7_lattices_type, type, (
% 160.68/103.17 v7_lattices: $i > $o)).
% 160.68/103.17 tff(v5_lattices_type, type, (
% 160.68/103.17 v5_lattices: $i > $o)).
% 160.68/103.17 tff(v4_lattices_type, type, (
% 160.68/103.17 v4_lattices: $i > $o)).
% 160.68/103.17 tff(r1_lattices_type, type, (
% 160.68/103.17 r1_lattices: ( $i * $i * $i ) > $o)).
% 160.68/103.17 tff(m1_relset_1_type, type, (
% 160.68/103.17 m1_relset_1: ( $i * $i * $i ) > $o)).
% 160.68/103.17 tff(k2_zfmisc_1_type, type, (
% 160.68/103.17 k2_zfmisc_1: ( $i * $i ) > $i)).
% 160.68/103.17 tff(m2_relset_1_type, type, (
% 160.68/103.17 m2_relset_1: ( $i * $i * $i ) > $o)).
% 160.68/103.17 tff(v1_funct_2_type, type, (
% 160.68/103.17 v1_funct_2: ( $i * $i * $i ) > $o)).
% 160.68/103.17 tff(v1_funct_1_type, type, (
% 160.68/103.17 v1_funct_1: $i > $o)).
% 160.68/103.17 tff(v1_xboole_0_type, type, (
% 160.68/103.17 v1_xboole_0: $i > $o)).
% 160.68/103.17 tff(l1_struct_0_type, type, (
% 160.68/103.17 l1_struct_0: $i > $o)).
% 160.68/103.17 tff(v2_binop_1_type, type, (
% 160.68/103.17 v2_binop_1: ( $i * $i ) > $o)).
% 160.68/103.17 tff(v1_partfun1_type, type, (
% 160.68/103.17 v1_partfun1: ( $i * $i * $i ) > $o)).
% 160.68/103.17 tff(v1_relat_1_type, type, (
% 160.68/103.17 v1_relat_1: $i > $o)).
% 160.68/103.17 tff(1,assumption,(m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))), introduced(assumption)).
% 160.68/103.17 tff(2,plain,
% 160.68/103.17 (^[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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> (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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))))),
% 160.68/103.17 inference(bind,[status(th)],[])).
% 160.68/103.17 tff(3,plain,
% 160.68/103.17 (![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> ![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 160.68/103.17 inference(quant_intro,[status(thm)],[2])).
% 160.68/103.17 tff(4,plain,
% 160.68/103.17 (^[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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> (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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))))),
% 160.68/103.17 inference(bind,[status(th)],[])).
% 160.68/103.17 tff(5,plain,
% 160.68/103.17 (![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> ![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 160.68/103.17 inference(quant_intro,[status(thm)],[4])).
% 160.68/103.17 tff(6,plain,
% 160.68/103.17 (![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> ![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 160.68/103.17 inference(transitivity,[status(thm)],[5, 3])).
% 160.68/103.17 tff(7,plain,
% 160.68/103.17 (^[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_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) <=> ((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))), ((((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))) <=> (((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C))))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))), rewrite((((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C))))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))) <=> (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))), ((((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))) <=> (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))), (((~((~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_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))) <=> ((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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))))), 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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> (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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))), (((~((~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_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))) <=> (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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))))),
% 160.68/103.17 inference(bind,[status(th)],[])).
% 160.68/103.17 tff(8,plain,
% 160.68/103.17 (![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_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))) <=> ![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 160.68/103.17 inference(quant_intro,[status(thm)],[7])).
% 160.68/103.17 tff(9,plain,
% 160.68/103.17 (![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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))) <=> ![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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(10,plain,
% 160.68/103.17 (^[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_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))), ((((((~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_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> (((~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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))), 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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))) <=> ((~((~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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))), ((((((~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_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ((~((~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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))))),
% 160.68/103.17 inference(bind,[status(th)],[])).
% 160.68/103.17 tff(11,plain,
% 160.68/103.17 (![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_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ![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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 160.68/103.17 inference(quant_intro,[status(thm)],[10])).
% 160.68/103.17 tff(12,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_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_2_0_filter_2')).
% 160.68/103.17 tff(13,plain,
% 160.68/103.17 (![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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[12, 11])).
% 160.68/103.17 tff(14,plain,
% 160.68/103.17 (![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_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[13, 9])).
% 160.68/103.17 tff(15,plain,(
% 160.68/103.17 ![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_2(B, C))) | (m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_12(C, B, A)) & r3_lattices(B, tptp_fun_D_12(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))))),
% 160.68/103.17 inference(skolemize,[status(sab)],[14])).
% 160.68/103.17 tff(16,plain,
% 160.68/103.17 (![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[15, 8])).
% 160.68/103.17 tff(17,plain,
% 160.68/103.17 (![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[16, 6])).
% 160.68/103.17 tff(18,plain,
% 160.68/103.17 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(19,plain,
% 160.68/103.17 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(20,plain,
% 160.68/103.17 ((~(~((~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))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(21,plain,
% 160.68/103.17 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))))),
% 160.68/103.17 inference(monotonicity,[status(thm)],[20, 19])).
% 160.68/103.17 tff(22,plain,
% 160.68/103.17 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))),
% 160.68/103.17 inference(transitivity,[status(thm)],[21, 18])).
% 160.68/103.17 tff(23,plain,
% 160.68/103.17 ((~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, 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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B)))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(24,plain,
% 160.68/103.17 ((~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B))) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, 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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B)))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(25,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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B))) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t31_filter_2')).
% 160.68/103.17 tff(26,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[25, 24])).
% 160.68/103.17 tff(27,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[26, 23])).
% 160.68/103.17 tff(28,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[27, 23])).
% 160.68/103.17 tff(29,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[28, 23])).
% 160.68/103.17 tff(30,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[29, 23])).
% 160.68/103.17 tff(31,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[30, 23])).
% 160.68/103.17 tff(32,plain,
% 160.68/103.17 (~![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, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[31, 23])).
% 160.68/103.17 tff(33,plain,
% 160.68/103.17 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))),
% 160.68/103.17 inference(modus_ponens,[status(thm)],[32, 22])).
% 160.68/103.17 tff(34,plain,
% 160.68/103.17 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 160.68/103.17 inference(and_elim,[status(thm)],[33])).
% 160.68/103.17 tff(35,plain,
% 160.68/103.17 (l3_lattices(A!0)),
% 160.68/103.17 inference(and_elim,[status(thm)],[33])).
% 160.68/103.17 tff(36,plain,
% 160.68/103.17 (v10_lattices(A!0)),
% 160.68/103.17 inference(and_elim,[status(thm)],[33])).
% 160.68/103.17 tff(37,plain,
% 160.68/103.17 (~v3_struct_0(A!0)),
% 160.68/103.17 inference(and_elim,[status(thm)],[33])).
% 160.68/103.17 tff(38,plain,
% 160.68/103.17 (((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | ((~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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(39,plain,
% 160.68/103.17 ((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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(40,plain,
% 160.68/103.17 ((~((~((~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, D, B!1))))))) <=> (~((~((~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))))))),
% 160.68/103.17 inference(rewrite,[status(thm)],[])).
% 160.68/103.17 tff(41,plain,
% 160.68/103.17 ((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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, D, B!1)))))))) <=> (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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))))))),
% 160.68/103.18 inference(monotonicity,[status(thm)],[40])).
% 160.68/103.18 tff(42,plain,
% 160.68/103.18 ((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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, D, B!1)))))))) <=> ((~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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))))))),
% 160.68/103.18 inference(transitivity,[status(thm)],[41, 39])).
% 160.68/103.18 tff(43,plain,
% 160.68/103.18 (((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, D, B!1))))))))) <=> ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | ((~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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))))))))),
% 160.68/103.18 inference(monotonicity,[status(thm)],[42])).
% 160.68/103.18 tff(44,plain,
% 160.68/103.18 (((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, D, B!1))))))))) <=> ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))))))),
% 160.68/103.18 inference(transitivity,[status(thm)],[43, 38])).
% 160.68/103.18 tff(45,plain,
% 160.68/103.18 ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(B!1 = D)) | (~r3_lattices(A!0, D, B!1))))))))),
% 160.68/103.18 inference(quant_inst,[status(thm)],[])).
% 160.68/103.18 tff(46,plain,
% 160.68/103.18 ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~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_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[45, 44])).
% 160.68/103.18 tff(47,plain,
% 160.68/103.18 (~((~((~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))))),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[46, 37, 36, 35, 34, 17])).
% 160.68/103.18 tff(48,plain,
% 160.68/103.18 (((~((~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, B!1), u1_struct_0(A!0))) | (~(B!1 = tptp_fun_D_12(B!1, A!0, B!1))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, B!1), B!1)))))) | (~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))))) | (r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))),
% 160.68/103.18 inference(tautology,[status(thm)],[])).
% 160.68/103.18 tff(49,plain,
% 160.68/103.18 (r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[48, 47])).
% 160.68/103.18 tff(50,plain,
% 160.68/103.18 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(51,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[50])).
% 160.68/103.18 tff(52,plain,
% 160.68/103.18 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(53,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[52])).
% 160.68/103.18 tff(54,plain,
% 160.68/103.18 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(55,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[54])).
% 160.68/103.18 tff(56,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 160.68/103.18 inference(transitivity,[status(thm)],[55, 53])).
% 160.68/103.18 tff(57,plain,
% 160.68/103.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(58,plain,
% 160.68/103.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[57])).
% 160.68/103.18 tff(59,plain,
% 160.68/103.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(60,plain,
% 160.68/103.18 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(61,plain,
% 160.68/103.18 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[60])).
% 160.68/103.18 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)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_filter_2')).
% 160.68/103.18 tff(63,plain,
% 160.68/103.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[62, 61])).
% 160.68/103.18 tff(64,plain,
% 160.68/103.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[63, 59])).
% 160.68/103.18 tff(65,plain,(
% 160.68/103.18 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(skolemize,[status(sab)],[64])).
% 160.68/103.18 tff(66,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[65, 58])).
% 160.68/103.18 tff(67,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[66, 56])).
% 160.68/103.18 tff(68,plain,
% 160.68/103.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[67, 51])).
% 160.68/103.18 tff(69,plain,
% 160.68/103.18 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(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))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(70,plain,
% 160.68/103.18 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 160.68/103.18 inference(quant_inst,[status(thm)],[])).
% 160.68/103.18 tff(71,plain,
% 160.68/103.18 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(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))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[70, 69])).
% 160.68/103.18 tff(72,plain,
% 160.68/103.18 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[71, 37, 36, 35, 68])).
% 160.68/103.18 tff(73,plain,
% 160.68/103.18 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(74,plain,
% 160.68/103.18 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 160.68/103.18 inference(quant_inst,[status(thm)],[])).
% 160.68/103.18 tff(75,plain,
% 160.68/103.18 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[74, 73])).
% 160.68/103.18 tff(76,plain,
% 160.68/103.18 (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[75, 34, 72])).
% 160.68/103.18 tff(77,plain,
% 160.68/103.18 (a_2_0_filter_2(A!0, B!1) = k18_filter_2(A!0, B!1)),
% 160.68/103.18 inference(symmetry,[status(thm)],[76])).
% 160.68/103.18 tff(78,plain,
% 160.68/103.18 (r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(B!1, k18_filter_2(A!0, B!1))),
% 160.68/103.18 inference(monotonicity,[status(thm)],[77])).
% 160.68/103.18 tff(79,plain,
% 160.68/103.18 (r2_hidden(B!1, k18_filter_2(A!0, B!1)) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))),
% 160.68/103.18 inference(symmetry,[status(thm)],[78])).
% 160.68/103.18 tff(80,plain,
% 160.68/103.18 ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) <=> (~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))),
% 160.68/103.18 inference(monotonicity,[status(thm)],[79])).
% 160.68/103.18 tff(81,plain,
% 160.68/103.18 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(82,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[81])).
% 160.68/103.18 tff(83,plain,
% 160.68/103.18 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(84,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[83])).
% 160.68/103.18 tff(85,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(86,plain,
% 160.68/103.18 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(87,plain,
% 160.68/103.18 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[86])).
% 160.68/103.18 tff(88,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 160.68/103.18 tff(89,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[88, 87])).
% 160.68/103.18 tff(90,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[89, 85])).
% 160.68/103.18 tff(91,plain,(
% 160.68/103.18 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 160.68/103.18 inference(skolemize,[status(sab)],[90])).
% 160.68/103.18 tff(92,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[91, 84])).
% 160.68/103.18 tff(93,plain,
% 160.68/103.18 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[92, 82])).
% 160.68/103.18 tff(94,plain,
% 160.68/103.18 (((~![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)))))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(95,plain,
% 160.68/103.18 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 160.68/103.18 inference(quant_inst,[status(thm)],[])).
% 160.68/103.18 tff(96,plain,
% 160.68/103.18 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[95, 94])).
% 160.68/103.18 tff(97,plain,
% 160.68/103.18 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[96, 35, 93])).
% 160.68/103.18 tff(98,plain,
% 160.68/103.18 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 160.68/103.18 inference(tautology,[status(thm)],[])).
% 160.68/103.18 tff(99,plain,
% 160.68/103.18 (l1_lattices(A!0)),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[98, 97])).
% 160.68/103.18 tff(100,plain,
% 160.68/103.18 (^[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))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(101,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[100])).
% 160.68/103.18 tff(102,plain,
% 160.68/103.18 (^[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)))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(103,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[102])).
% 160.68/103.18 tff(104,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(105,plain,
% 160.68/103.18 (^[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)))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(106,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[105])).
% 160.68/103.18 tff(107,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/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 160.68/103.18 tff(108,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[107, 106])).
% 160.68/103.18 tff(109,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[108, 104])).
% 160.68/103.18 tff(110,plain,(
% 160.68/103.18 ![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)))),
% 160.68/103.18 inference(skolemize,[status(sab)],[109])).
% 160.68/103.18 tff(111,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[110, 103])).
% 160.68/103.18 tff(112,plain,
% 160.68/103.18 (![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)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[111, 101])).
% 160.68/103.18 tff(113,plain,
% 160.68/103.18 (((~![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)))))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(114,plain,
% 160.68/103.18 ((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)))))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(115,plain,
% 160.68/103.18 (((~![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))))))),
% 160.68/103.18 inference(monotonicity,[status(thm)],[114])).
% 160.68/103.18 tff(116,plain,
% 160.68/103.18 (((~![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)))))),
% 160.68/103.18 inference(transitivity,[status(thm)],[115, 113])).
% 160.68/103.18 tff(117,plain,
% 160.68/103.18 ((~![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)))),
% 160.68/103.18 inference(quant_inst,[status(thm)],[])).
% 160.68/103.18 tff(118,plain,
% 160.68/103.18 ((~![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))))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[117, 116])).
% 160.68/103.18 tff(119,plain,
% 160.68/103.18 (~(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)))),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[118, 37, 36, 35, 112])).
% 160.68/103.18 tff(120,plain,
% 160.68/103.18 ((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)),
% 160.68/103.18 inference(tautology,[status(thm)],[])).
% 160.68/103.18 tff(121,plain,
% 160.68/103.18 (v6_lattices(A!0)),
% 160.68/103.18 inference(unit_resolution,[status(thm)],[120, 119])).
% 160.68/103.18 tff(122,plain,
% 160.68/103.18 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(123,plain,
% 160.68/103.18 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[122])).
% 160.68/103.18 tff(124,plain,
% 160.68/103.18 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(125,plain,
% 160.68/103.18 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[124])).
% 160.68/103.18 tff(126,plain,
% 160.68/103.18 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 160.68/103.18 inference(rewrite,[status(thm)],[])).
% 160.68/103.18 tff(127,plain,
% 160.68/103.18 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_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) & l1_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) & l1_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) & l1_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)) & l1_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) & l1_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)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))))),
% 160.68/103.18 inference(bind,[status(th)],[])).
% 160.68/103.18 tff(128,plain,
% 160.68/103.18 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 160.68/103.18 inference(quant_intro,[status(thm)],[127])).
% 160.68/103.18 tff(129,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 160.68/103.18 tff(130,plain,
% 160.68/103.18 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[129, 128])).
% 160.68/103.18 tff(131,plain,
% 160.68/103.18 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 160.68/103.18 inference(modus_ponens,[status(thm)],[130, 126])).
% 160.68/103.18 tff(132,plain,(
% 160.68/103.18 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 160.68/103.19 inference(skolemize,[status(sab)],[131])).
% 160.68/103.19 tff(133,plain,
% 160.68/103.19 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[132, 125])).
% 160.68/103.19 tff(134,plain,
% 160.68/103.19 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[133, 123])).
% 160.68/103.19 tff(135,plain,
% 160.68/103.19 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))),
% 160.68/103.19 inference(and_elim,[status(thm)],[33])).
% 160.68/103.19 tff(136,plain,
% 160.68/103.19 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 160.68/103.19 inference(or_elim,[status(thm)],[135])).
% 160.68/103.19 tff(137,plain,
% 160.68/103.19 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(138,plain,
% 160.68/103.19 ((v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(139,plain,
% 160.68/103.19 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1))))),
% 160.68/103.19 inference(monotonicity,[status(thm)],[138])).
% 160.68/103.19 tff(140,plain,
% 160.68/103.19 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))),
% 160.68/103.19 inference(transitivity,[status(thm)],[139, 137])).
% 160.68/103.19 tff(141,plain,
% 160.68/103.19 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 160.68/103.19 inference(quant_inst,[status(thm)],[])).
% 160.68/103.19 tff(142,plain,
% 160.68/103.19 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[141, 140])).
% 160.68/103.19 tff(143,plain,
% 160.68/103.19 (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)),
% 160.68/103.19 inference(unit_resolution,[status(thm)],[142, 37, 34, 136, 134, 121, 99])).
% 160.68/103.19 tff(144,plain,
% 160.68/103.19 (k2_lattices(A!0, C!2, B!1) = k4_lattices(A!0, C!2, B!1)),
% 160.68/103.19 inference(symmetry,[status(thm)],[143])).
% 160.68/103.19 tff(145,plain,
% 160.68/103.19 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))),
% 160.68/103.19 inference(bind,[status(th)],[])).
% 160.68/103.19 tff(146,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(quant_intro,[status(thm)],[145])).
% 160.68/103.19 tff(147,plain,
% 160.68/103.19 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 160.68/103.19 inference(bind,[status(th)],[])).
% 160.68/103.19 tff(148,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 160.68/103.19 inference(quant_intro,[status(thm)],[147])).
% 160.68/103.19 tff(149,plain,
% 160.68/103.19 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 160.68/103.19 inference(bind,[status(th)],[])).
% 160.68/103.19 tff(150,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 160.68/103.19 inference(quant_intro,[status(thm)],[149])).
% 160.68/103.19 tff(151,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 160.68/103.19 inference(transitivity,[status(thm)],[150, 148])).
% 160.68/103.19 tff(152,plain,
% 160.68/103.19 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))))),
% 160.68/103.19 inference(bind,[status(th)],[])).
% 160.68/103.19 tff(153,plain,
% 160.68/103.19 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 160.68/103.19 inference(quant_intro,[status(thm)],[152])).
% 160.68/103.19 tff(154,plain,
% 160.68/103.19 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(155,plain,
% 160.68/103.19 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))))),
% 160.68/103.19 inference(bind,[status(th)],[])).
% 160.68/103.19 tff(156,plain,
% 160.68/103.19 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(quant_intro,[status(thm)],[155])).
% 160.68/103.19 tff(157,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattices')).
% 160.68/103.19 tff(158,plain,
% 160.68/103.19 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[157, 156])).
% 160.68/103.19 tff(159,plain,
% 160.68/103.19 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[158, 154])).
% 160.68/103.19 tff(160,plain,(
% 160.68/103.19 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(skolemize,[status(sab)],[159])).
% 160.68/103.19 tff(161,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[160, 153])).
% 160.68/103.19 tff(162,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[161, 151])).
% 160.68/103.19 tff(163,plain,
% 160.68/103.19 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[162, 146])).
% 160.68/103.19 tff(164,plain,
% 160.68/103.19 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_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))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_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))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(165,plain,
% 160.68/103.19 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_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))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 160.68/103.19 inference(quant_inst,[status(thm)],[])).
% 160.68/103.19 tff(166,plain,
% 160.68/103.19 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_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))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[165, 164])).
% 160.68/103.19 tff(167,plain,
% 160.68/103.19 ((~l1_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))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 160.68/103.19 inference(unit_resolution,[status(thm)],[166, 37, 163])).
% 160.68/103.19 tff(168,plain,
% 160.68/103.19 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 160.68/103.19 inference(unit_resolution,[status(thm)],[167, 99])).
% 160.68/103.19 tff(169,plain,
% 160.68/103.19 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C))))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(170,plain,
% 160.68/103.19 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C))))),
% 160.68/103.19 inference(quant_inst,[status(thm)],[])).
% 160.68/103.19 tff(171,plain,
% 160.68/103.19 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[170, 169])).
% 160.68/103.19 tff(172,plain,
% 160.68/103.19 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))),
% 160.68/103.19 inference(unit_resolution,[status(thm)],[171, 136, 168])).
% 160.68/103.19 tff(173,plain,
% 160.68/103.19 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(174,plain,
% 160.68/103.19 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))),
% 160.68/103.19 inference(quant_inst,[status(thm)],[])).
% 160.68/103.19 tff(175,plain,
% 160.68/103.19 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[174, 173])).
% 160.68/103.19 tff(176,plain,
% 160.68/103.19 (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)),
% 160.68/103.19 inference(unit_resolution,[status(thm)],[175, 34, 172])).
% 160.68/103.19 tff(177,plain,
% 160.68/103.19 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_lattices(A!0, C!2, B!1)),
% 160.68/103.19 inference(symmetry,[status(thm)],[176])).
% 160.68/103.19 tff(178,plain,
% 160.68/103.19 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k4_lattices(A!0, C!2, B!1)),
% 160.68/103.19 inference(transitivity,[status(thm)],[177, 144])).
% 160.68/103.19 tff(179,plain,
% 160.68/103.19 (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))),
% 160.68/103.19 inference(monotonicity,[status(thm)],[178, 77])).
% 160.68/103.19 tff(180,plain,
% 160.68/103.19 (r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))),
% 160.68/103.19 inference(symmetry,[status(thm)],[179])).
% 160.68/103.19 tff(181,plain,
% 160.68/103.19 ((~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))) <=> (~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))),
% 160.68/103.19 inference(monotonicity,[status(thm)],[180])).
% 160.68/103.19 tff(182,assumption,(~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))), introduced(assumption)).
% 160.68/103.19 tff(183,plain,
% 160.68/103.19 (~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))),
% 160.68/103.19 inference(modus_ponens,[status(thm)],[182, 181])).
% 160.68/103.19 tff(184,plain,
% 160.68/103.19 (((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | ((~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))))) <=> ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(185,plain,
% 160.68/103.19 ((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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1))))))))) <=> ((~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(186,plain,
% 160.68/103.19 ((~((~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))) | (~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)) | (~r3_lattices(A!0, D, B!1))))))) <=> (~((~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1))))))))),
% 160.68/103.19 inference(rewrite,[status(thm)],[])).
% 160.68/103.19 tff(187,plain,
% 160.68/103.19 ((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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))) | (~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)) | (~r3_lattices(A!0, D, B!1)))))))) <=> (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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))))),
% 160.68/103.20 inference(monotonicity,[status(thm)],[186])).
% 160.68/103.20 tff(188,plain,
% 160.68/103.20 ((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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))) | (~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)) | (~r3_lattices(A!0, D, B!1)))))))) <=> ((~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))))),
% 160.68/103.20 inference(transitivity,[status(thm)],[187, 185])).
% 160.68/103.20 tff(189,plain,
% 160.68/103.20 (((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))) | (~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)) | (~r3_lattices(A!0, D, B!1))))))))) <=> ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | ((~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1))))))))))),
% 160.68/103.20 inference(monotonicity,[status(thm)],[188])).
% 160.68/103.20 tff(190,plain,
% 160.68/103.20 (((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))) | (~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)) | (~r3_lattices(A!0, D, B!1))))))))) <=> ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))))),
% 160.72/103.20 inference(transitivity,[status(thm)],[189, 184])).
% 160.72/103.20 tff(191,plain,
% 160.72/103.20 ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))) | (~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)) | (~r3_lattices(A!0, D, B!1))))))))),
% 160.72/103.20 inference(quant_inst,[status(thm)],[])).
% 160.72/103.20 tff(192,plain,
% 160.72/103.20 ((~![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_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_12(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_12(C, B, A))) | (~r3_lattices(B, tptp_fun_D_12(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1))))))))),
% 160.72/103.20 inference(modus_ponens,[status(thm)],[191, 190])).
% 160.72/103.20 tff(193,plain,
% 160.72/103.20 (~((~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1)))))))),
% 160.72/103.20 inference(unit_resolution,[status(thm)],[192, 37, 36, 35, 34, 17])).
% 160.72/103.20 tff(194,plain,
% 160.72/103.20 (((~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | (~((~r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) | (~r3_lattices(A!0, tptp_fun_D_12(B!1, A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), B!1))))))) | (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))),
% 160.72/103.20 inference(tautology,[status(thm)],[])).
% 160.72/103.20 tff(195,plain,
% 160.72/103.20 (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))),
% 160.72/103.20 inference(unit_resolution,[status(thm)],[194, 193])).
% 160.72/103.20 tff(196,assumption,(![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))), introduced(assumption)).
% 160.72/103.20 tff(197,plain,
% 160.72/103.20 (^[A: $i, B: $i, C: $i] : refl(((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 160.72/103.20 inference(bind,[status(th)],[])).
% 160.72/103.20 tff(198,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.20 inference(quant_intro,[status(thm)],[197])).
% 160.72/103.20 tff(199,plain,
% 160.72/103.20 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 160.72/103.20 inference(bind,[status(th)],[])).
% 160.72/103.20 tff(200,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.20 inference(quant_intro,[status(thm)],[199])).
% 160.72/103.20 tff(201,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 160.72/103.20 inference(rewrite,[status(thm)],[])).
% 160.72/103.20 tff(202,plain,
% 160.72/103.20 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_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) & l1_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) & l1_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) & l1_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)) & l1_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) & l1_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)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))))),
% 160.72/103.20 inference(bind,[status(th)],[])).
% 160.72/103.20 tff(203,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 160.72/103.20 inference(quant_intro,[status(thm)],[202])).
% 160.72/103.20 tff(204,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 160.72/103.20 tff(205,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 160.72/103.20 inference(modus_ponens,[status(thm)],[204, 203])).
% 160.72/103.20 tff(206,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 160.72/103.20 inference(modus_ponens,[status(thm)],[205, 201])).
% 160.72/103.20 tff(207,plain,(
% 160.72/103.20 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 160.72/103.20 inference(skolemize,[status(sab)],[206])).
% 160.72/103.20 tff(208,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.20 inference(modus_ponens,[status(thm)],[207, 200])).
% 160.72/103.20 tff(209,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.20 inference(modus_ponens,[status(thm)],[208, 198])).
% 160.72/103.20 tff(210,plain,
% 160.72/103.20 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))),
% 160.72/103.20 inference(rewrite,[status(thm)],[])).
% 160.72/103.20 tff(211,plain,
% 160.72/103.20 (((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))),
% 160.72/103.20 inference(rewrite,[status(thm)],[])).
% 160.72/103.20 tff(212,plain,
% 160.72/103.20 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2))))),
% 160.72/103.20 inference(monotonicity,[status(thm)],[211])).
% 160.72/103.20 tff(213,plain,
% 160.72/103.20 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))),
% 160.72/103.20 inference(transitivity,[status(thm)],[212, 210])).
% 160.72/103.20 tff(214,plain,
% 160.72/103.20 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 160.72/103.20 inference(quant_inst,[status(thm)],[])).
% 160.72/103.20 tff(215,plain,
% 160.72/103.20 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2))),
% 160.72/103.20 inference(modus_ponens,[status(thm)],[214, 213])).
% 160.72/103.20 tff(216,plain,
% 160.72/103.20 (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)),
% 160.72/103.20 inference(unit_resolution,[status(thm)],[215, 37, 34, 136, 209, 121, 99])).
% 160.72/103.20 tff(217,plain,
% 160.72/103.20 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k4_lattices(A!0, B!1, C!2)),
% 160.72/103.20 inference(transitivity,[status(thm)],[177, 144, 216])).
% 160.72/103.20 tff(218,plain,
% 160.72/103.20 (r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1) <=> r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 160.72/103.20 inference(monotonicity,[status(thm)],[217])).
% 160.72/103.20 tff(219,plain,
% 160.72/103.20 (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)),
% 160.72/103.20 inference(symmetry,[status(thm)],[218])).
% 160.72/103.20 tff(220,plain,
% 160.72/103.20 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 160.72/103.20 inference(bind,[status(th)],[])).
% 160.72/103.20 tff(221,plain,
% 160.72/103.20 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.20 inference(quant_intro,[status(thm)],[220])).
% 160.72/103.20 tff(222,plain,
% 160.72/103.20 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(223,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[222])).
% 160.72/103.21 tff(224,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(225,plain,
% 160.72/103.21 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_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) & l1_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) & l1_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) & l1_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)) & l1_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) & l1_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)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(226,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[225])).
% 160.72/103.21 tff(227,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_lattices')).
% 160.72/103.21 tff(228,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[227, 226])).
% 160.72/103.21 tff(229,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[228, 224])).
% 160.72/103.21 tff(230,plain,(
% 160.72/103.21 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 160.72/103.21 inference(skolemize,[status(sab)],[229])).
% 160.72/103.21 tff(231,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[230, 223])).
% 160.72/103.21 tff(232,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[231, 221])).
% 160.72/103.21 tff(233,plain,
% 160.72/103.21 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(234,plain,
% 160.72/103.21 ((v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(235,plain,
% 160.72/103.21 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 160.72/103.21 inference(monotonicity,[status(thm)],[234])).
% 160.72/103.21 tff(236,plain,
% 160.72/103.21 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 160.72/103.21 inference(transitivity,[status(thm)],[235, 233])).
% 160.72/103.21 tff(237,plain,
% 160.72/103.21 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 160.72/103.21 inference(quant_inst,[status(thm)],[])).
% 160.72/103.21 tff(238,plain,
% 160.72/103.21 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[237, 236])).
% 160.72/103.21 tff(239,plain,
% 160.72/103.21 (m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[238, 37, 34, 136, 232, 121, 99])).
% 160.72/103.21 tff(240,plain,
% 160.72/103.21 ((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)),
% 160.72/103.21 inference(tautology,[status(thm)],[])).
% 160.72/103.21 tff(241,plain,
% 160.72/103.21 (v9_lattices(A!0)),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[240, 119])).
% 160.72/103.21 tff(242,plain,
% 160.72/103.21 ((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)),
% 160.72/103.21 inference(tautology,[status(thm)],[])).
% 160.72/103.21 tff(243,plain,
% 160.72/103.21 (v8_lattices(A!0)),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[242, 119])).
% 160.72/103.21 tff(244,plain,
% 160.72/103.21 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(245,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[244])).
% 160.72/103.21 tff(246,plain,
% 160.72/103.21 (^[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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(247,plain,
% 160.72/103.21 (![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, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[246])).
% 160.72/103.21 tff(248,plain,
% 160.72/103.21 (![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, C) <=> r1_lattices(A, B, C))) <=> ![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, C) <=> r1_lattices(A, B, C)))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(249,plain,
% 160.72/103.21 (^[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, C) <=> r1_lattices(A, B, C))) <=> (((~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, C) <=> r1_lattices(A, B, C))))), 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, C) <=> r1_lattices(A, B, C))) <=> ((~((~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, C) <=> r1_lattices(A, B, C)))), (((((((((~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, C) <=> r1_lattices(A, B, C))) <=> ((~((~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, C) <=> r1_lattices(A, B, C)))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(250,plain,
% 160.72/103.21 (![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, C) <=> r1_lattices(A, B, C))) <=> ![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, C) <=> r1_lattices(A, B, C)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[249])).
% 160.72/103.21 tff(251,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, C) <=> r1_lattices(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 160.72/103.21 tff(252,plain,
% 160.72/103.21 (![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, C) <=> r1_lattices(A, B, C)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[251, 250])).
% 160.72/103.21 tff(253,plain,
% 160.72/103.21 (![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, C) <=> r1_lattices(A, B, C)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[252, 248])).
% 160.72/103.21 tff(254,plain,(
% 160.72/103.21 ![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, C) <=> r1_lattices(A, B, C)))),
% 160.72/103.21 inference(skolemize,[status(sab)],[253])).
% 160.72/103.21 tff(255,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[254, 247])).
% 160.72/103.21 tff(256,plain,
% 160.72/103.21 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[255, 245])).
% 160.72/103.21 tff(257,plain,
% 160.72/103.21 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(258,plain,
% 160.72/103.21 ((v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_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)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(259,plain,
% 160.72/103.21 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))))),
% 160.72/103.21 inference(monotonicity,[status(thm)],[258])).
% 160.72/103.21 tff(260,plain,
% 160.72/103.21 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 160.72/103.21 inference(transitivity,[status(thm)],[259, 257])).
% 160.72/103.21 tff(261,plain,
% 160.72/103.21 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))),
% 160.72/103.21 inference(quant_inst,[status(thm)],[])).
% 160.72/103.21 tff(262,plain,
% 160.72/103.21 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[261, 260])).
% 160.72/103.21 tff(263,plain,
% 160.72/103.21 ((r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[262, 37, 35, 34, 256, 121, 243, 241])).
% 160.72/103.21 tff(264,plain,
% 160.72/103.21 (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[263, 239])).
% 160.72/103.21 tff(265,plain,
% 160.72/103.21 (^[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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(266,plain,
% 160.72/103.21 (![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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[265])).
% 160.72/103.21 tff(267,plain,
% 160.72/103.21 (^[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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(268,plain,
% 160.72/103.21 (![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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[267])).
% 160.72/103.21 tff(269,plain,
% 160.72/103.21 (^[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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(270,plain,
% 160.72/103.21 (![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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[269])).
% 160.72/103.21 tff(271,plain,
% 160.72/103.21 (![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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 160.72/103.21 inference(transitivity,[status(thm)],[270, 268])).
% 160.72/103.21 tff(272,plain,
% 160.72/103.21 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, 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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, 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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(273,plain,
% 160.72/103.21 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, 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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[272])).
% 160.72/103.21 tff(274,plain,
% 160.72/103.21 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(275,plain,
% 160.72/103.21 (^[A: $i] : 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)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_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)) => r1_lattices(A, k4_lattices(A, B, C), B)) <=> ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_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)) => r1_lattices(A, k4_lattices(A, B, C), B)))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B)))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_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)) => r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))))),
% 160.72/103.21 inference(bind,[status(th)],[])).
% 160.72/103.21 tff(276,plain,
% 160.72/103.21 (![A: $i] : (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_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)) => r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(quant_intro,[status(thm)],[275])).
% 160.72/103.21 tff(277,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_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)) => r1_lattices(A, k4_lattices(A, B, C), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_lattices')).
% 160.72/103.21 tff(278,plain,
% 160.72/103.21 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[277, 276])).
% 160.72/103.21 tff(279,plain,
% 160.72/103.21 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[278, 274])).
% 160.72/103.21 tff(280,plain,(
% 160.72/103.21 ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_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))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(skolemize,[status(sab)],[279])).
% 160.72/103.21 tff(281,plain,
% 160.72/103.21 (![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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[280, 273])).
% 160.72/103.21 tff(282,plain,
% 160.72/103.21 (![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))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[281, 271])).
% 160.72/103.21 tff(283,plain,
% 160.72/103.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[282, 266])).
% 160.72/103.21 tff(284,plain,
% 160.72/103.21 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_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))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_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))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B))))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.21 tff(285,plain,
% 160.72/103.21 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_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))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B))))),
% 160.72/103.21 inference(quant_inst,[status(thm)],[])).
% 160.72/103.21 tff(286,plain,
% 160.72/103.21 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_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))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))),
% 160.72/103.21 inference(modus_ponens,[status(thm)],[285, 284])).
% 160.72/103.21 tff(287,plain,
% 160.72/103.21 ((~v6_lattices(A!0)) | (~v8_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))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[286, 37, 35, 283])).
% 160.72/103.21 tff(288,plain,
% 160.72/103.21 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))),
% 160.72/103.21 inference(unit_resolution,[status(thm)],[287, 243, 121])).
% 160.72/103.21 tff(289,plain,
% 160.72/103.21 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, 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))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1)))),
% 160.72/103.21 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(290,plain,
% 160.72/103.22 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1)))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(291,plain,
% 160.72/103.22 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[290, 289])).
% 160.72/103.22 tff(292,plain,
% 160.72/103.22 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[291, 34, 288])).
% 160.72/103.22 tff(293,plain,
% 160.72/103.22 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(294,plain,
% 160.72/103.22 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(295,plain,
% 160.72/103.22 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[294, 293])).
% 160.72/103.22 tff(296,plain,
% 160.72/103.22 (r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[295, 136, 292])).
% 160.72/103.22 tff(297,plain,
% 160.72/103.22 ((~(r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))) | r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) | (~r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(298,plain,
% 160.72/103.22 ((~(r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))) | r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[297, 296])).
% 160.72/103.22 tff(299,plain,
% 160.72/103.22 (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[298, 264])).
% 160.72/103.22 tff(300,plain,
% 160.72/103.22 (r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[299, 219])).
% 160.72/103.22 tff(301,plain,
% 160.72/103.22 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(302,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[301])).
% 160.72/103.22 tff(303,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(304,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 160.72/103.22 tff(305,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[304, 303])).
% 160.72/103.22 tff(306,plain,(
% 160.72/103.22 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 160.72/103.22 inference(skolemize,[status(sab)],[305])).
% 160.72/103.22 tff(307,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[306, 302])).
% 160.72/103.22 tff(308,plain,
% 160.72/103.22 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(309,plain,
% 160.72/103.22 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[308, 307])).
% 160.72/103.22 tff(310,plain,
% 160.72/103.22 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(311,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[310])).
% 160.72/103.22 tff(312,plain,
% 160.72/103.22 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(313,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[312])).
% 160.72/103.22 tff(314,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(315,plain,
% 160.72/103.22 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(316,plain,
% 160.72/103.22 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[315])).
% 160.72/103.22 tff(317,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 160.72/103.22 tff(318,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[317, 316])).
% 160.72/103.22 tff(319,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[318, 314])).
% 160.72/103.22 tff(320,plain,(
% 160.72/103.22 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(skolemize,[status(sab)],[319])).
% 160.72/103.22 tff(321,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[320, 313])).
% 160.72/103.22 tff(322,plain,
% 160.72/103.22 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[321, 311])).
% 160.72/103.22 tff(323,plain,
% 160.72/103.22 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(324,plain,
% 160.72/103.22 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(325,plain,
% 160.72/103.22 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[324, 323])).
% 160.72/103.22 tff(326,plain,
% 160.72/103.22 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[325, 322])).
% 160.72/103.22 tff(327,plain,
% 160.72/103.22 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[326, 99])).
% 160.72/103.22 tff(328,plain,
% 160.72/103.22 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(329,plain,
% 160.72/103.22 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[328, 327])).
% 160.72/103.22 tff(330,plain,
% 160.72/103.22 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(331,plain,
% 160.72/103.22 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[330, 329])).
% 160.72/103.22 tff(332,plain,
% 160.72/103.22 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[331, 309])).
% 160.72/103.22 tff(333,plain,
% 160.72/103.22 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(334,plain,
% 160.72/103.22 (l2_lattices(A!0)),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[333, 97])).
% 160.72/103.22 tff(335,plain,
% 160.72/103.22 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(336,plain,
% 160.72/103.22 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[335])).
% 160.72/103.22 tff(337,plain,
% 160.72/103.22 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(338,plain,
% 160.72/103.22 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(339,plain,
% 160.72/103.22 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[338])).
% 160.72/103.22 tff(340,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 160.72/103.22 tff(341,plain,
% 160.72/103.22 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[340, 339])).
% 160.72/103.22 tff(342,plain,
% 160.72/103.22 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[341, 337])).
% 160.72/103.22 tff(343,plain,(
% 160.72/103.22 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(skolemize,[status(sab)],[342])).
% 160.72/103.22 tff(344,plain,
% 160.72/103.22 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[343, 336])).
% 160.72/103.22 tff(345,plain,
% 160.72/103.22 (((~![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)))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(346,plain,
% 160.72/103.22 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(347,plain,
% 160.72/103.22 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[346, 345])).
% 160.72/103.22 tff(348,plain,
% 160.72/103.22 (l1_struct_0(A!0)),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[347, 344, 334])).
% 160.72/103.22 tff(349,plain,
% 160.72/103.22 (^[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))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(350,plain,
% 160.72/103.22 (![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)))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[349])).
% 160.72/103.22 tff(351,plain,
% 160.72/103.22 (^[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)))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(352,plain,
% 160.72/103.22 (![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)))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[351])).
% 160.72/103.22 tff(353,plain,
% 160.72/103.22 (![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))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(354,plain,
% 160.72/103.22 (^[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)))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(355,plain,
% 160.72/103.22 (![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))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[354])).
% 160.72/103.22 tff(356,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 160.72/103.22 tff(357,plain,
% 160.72/103.22 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[356, 355])).
% 160.72/103.22 tff(358,plain,
% 160.72/103.22 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[357, 353])).
% 160.72/103.22 tff(359,plain,(
% 160.72/103.22 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 160.72/103.22 inference(skolemize,[status(sab)],[358])).
% 160.72/103.22 tff(360,plain,
% 160.72/103.22 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[359, 352])).
% 160.72/103.22 tff(361,plain,
% 160.72/103.22 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[360, 350])).
% 160.72/103.22 tff(362,plain,
% 160.72/103.22 (((~![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))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(363,plain,
% 160.72/103.22 ((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))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(364,plain,
% 160.72/103.22 (((~![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)))))),
% 160.72/103.22 inference(monotonicity,[status(thm)],[363])).
% 160.72/103.22 tff(365,plain,
% 160.72/103.22 (((~![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))))),
% 160.72/103.22 inference(transitivity,[status(thm)],[364, 362])).
% 160.72/103.22 tff(366,plain,
% 160.72/103.22 ((~![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)))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(367,plain,
% 160.72/103.22 ((~![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)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[366, 365])).
% 160.72/103.22 tff(368,plain,
% 160.72/103.22 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[367, 37, 361])).
% 160.72/103.22 tff(369,plain,
% 160.72/103.22 (~v1_xboole_0(u1_struct_0(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[368, 348])).
% 160.72/103.22 tff(370,plain,
% 160.72/103.22 ((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))) | v7_lattices(A!0)),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(371,plain,
% 160.72/103.22 (v7_lattices(A!0)),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[370, 119])).
% 160.72/103.22 tff(372,plain,
% 160.72/103.22 (^[A: $i] : refl((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(373,plain,
% 160.72/103.22 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[372])).
% 160.72/103.22 tff(374,plain,
% 160.72/103.22 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))), ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)))), ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))), rewrite((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(375,plain,
% 160.72/103.22 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[374])).
% 160.72/103.22 tff(376,plain,
% 160.72/103.22 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(377,plain,
% 160.72/103.22 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(378,plain,
% 160.72/103.22 (![A: $i] : ((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[377])).
% 160.72/103.22 tff(379,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A))) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc5_lattice2')).
% 160.72/103.22 tff(380,plain,
% 160.72/103.22 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[379, 378])).
% 160.72/103.22 tff(381,plain,
% 160.72/103.22 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[380, 376])).
% 160.72/103.22 tff(382,plain,(
% 160.72/103.22 ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_lattices(A)) & v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 160.72/103.22 inference(skolemize,[status(sab)],[381])).
% 160.72/103.22 tff(383,plain,
% 160.72/103.22 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[382, 375])).
% 160.72/103.22 tff(384,plain,
% 160.72/103.22 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[383, 373])).
% 160.72/103.22 tff(385,plain,
% 160.72/103.22 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(386,plain,
% 160.72/103.22 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 160.72/103.22 inference(quant_inst,[status(thm)],[])).
% 160.72/103.22 tff(387,plain,
% 160.72/103.22 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[386, 385])).
% 160.72/103.22 tff(388,plain,
% 160.72/103.22 ((~l1_lattices(A!0)) | (~v7_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[387, 37, 384])).
% 160.72/103.22 tff(389,plain,
% 160.72/103.22 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[388, 99, 371])).
% 160.72/103.22 tff(390,plain,
% 160.72/103.22 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(391,plain,
% 160.72/103.22 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[390, 389])).
% 160.72/103.22 tff(392,plain,
% 160.72/103.22 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 160.72/103.22 inference(tautology,[status(thm)],[])).
% 160.72/103.22 tff(393,plain,
% 160.72/103.22 (v1_funct_1(u1_lattices(A!0))),
% 160.72/103.22 inference(unit_resolution,[status(thm)],[392, 389])).
% 160.72/103.22 tff(394,plain,
% 160.72/103.22 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(395,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[394])).
% 160.72/103.22 tff(396,plain,
% 160.72/103.22 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) <=> (~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))))), rewrite((~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)))), rewrite(((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(397,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[396])).
% 160.72/103.22 tff(398,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(399,plain,
% 160.72/103.22 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))))),
% 160.72/103.22 inference(bind,[status(th)],[])).
% 160.72/103.22 tff(400,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 160.72/103.22 inference(quant_intro,[status(thm)],[399])).
% 160.72/103.22 tff(401,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_binop_1')).
% 160.72/103.22 tff(402,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[401, 400])).
% 160.72/103.22 tff(403,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[402, 398])).
% 160.72/103.22 tff(404,plain,(
% 160.72/103.22 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 160.72/103.22 inference(skolemize,[status(sab)],[403])).
% 160.72/103.22 tff(405,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[404, 397])).
% 160.72/103.22 tff(406,plain,
% 160.72/103.22 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 160.72/103.22 inference(modus_ponens,[status(thm)],[405, 395])).
% 160.72/103.22 tff(407,plain,
% 160.72/103.22 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))),
% 160.72/103.22 inference(rewrite,[status(thm)],[])).
% 160.72/103.22 tff(408,plain,
% 160.72/103.22 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(409,plain,
% 160.72/103.23 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))),
% 160.72/103.23 inference(monotonicity,[status(thm)],[408])).
% 160.72/103.23 tff(410,plain,
% 160.72/103.23 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))),
% 160.72/103.23 inference(transitivity,[status(thm)],[409, 407])).
% 160.72/103.23 tff(411,plain,
% 160.72/103.23 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 160.72/103.23 inference(quant_inst,[status(thm)],[])).
% 160.72/103.23 tff(412,plain,
% 160.72/103.23 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))),
% 160.72/103.23 inference(modus_ponens,[status(thm)],[411, 410])).
% 160.72/103.23 tff(413,plain,
% 160.72/103.23 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[412, 34, 136, 406, 393, 391, 369, 332])).
% 160.72/103.23 tff(414,plain,
% 160.72/103.23 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(415,plain,
% 160.72/103.23 (((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | $false) <=> ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(416,plain,
% 160.72/103.23 ((~$true) <=> $false),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(417,plain,
% 160.72/103.23 ((k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)) <=> $true),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(418,plain,
% 160.72/103.23 ((~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))) <=> (~$true)),
% 160.72/103.23 inference(monotonicity,[status(thm)],[417])).
% 160.72/103.23 tff(419,plain,
% 160.72/103.23 ((~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))) <=> $false),
% 160.72/103.23 inference(transitivity,[status(thm)],[418, 416])).
% 160.72/103.23 tff(420,plain,
% 160.72/103.23 (((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) <=> ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | $false)),
% 160.72/103.23 inference(monotonicity,[status(thm)],[419])).
% 160.72/103.23 tff(421,plain,
% 160.72/103.23 (((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) <=> ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))),
% 160.72/103.23 inference(transitivity,[status(thm)],[420, 415])).
% 160.72/103.23 tff(422,plain,
% 160.72/103.23 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))))),
% 160.72/103.23 inference(monotonicity,[status(thm)],[421])).
% 160.72/103.23 tff(423,plain,
% 160.72/103.23 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))),
% 160.72/103.23 inference(transitivity,[status(thm)],[422, 414])).
% 160.72/103.23 tff(424,plain,
% 160.72/103.23 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))))),
% 160.72/103.23 inference(quant_inst,[status(thm)],[])).
% 160.72/103.23 tff(425,plain,
% 160.72/103.23 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))),
% 160.72/103.23 inference(modus_ponens,[status(thm)],[424, 423])).
% 160.72/103.23 tff(426,plain,
% 160.72/103.23 ($false),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[425, 413, 300, 196])).
% 160.72/103.23 tff(427,plain,(~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))), inference(lemma,lemma(discharge,[]))).
% 160.72/103.23 tff(428,plain,
% 160.72/103.23 ((~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D)))),
% 160.72/103.23 inference(tautology,[status(thm)],[])).
% 160.72/103.23 tff(429,plain,
% 160.72/103.23 ((~(r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = D))))) | r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[428, 427])).
% 160.72/103.23 tff(430,plain,
% 160.72/103.23 (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[429, 195])).
% 160.72/103.23 tff(431,plain,
% 160.72/103.23 ($false),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[430, 183])).
% 160.72/103.23 tff(432,plain,(r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))), inference(lemma,lemma(discharge,[]))).
% 160.72/103.23 tff(433,plain,
% 160.72/103.23 (k4_lattices(A!0, B!1, C!2) = k4_lattices(A!0, C!2, B!1)),
% 160.72/103.23 inference(symmetry,[status(thm)],[216])).
% 160.72/103.23 tff(434,plain,
% 160.72/103.23 (r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))),
% 160.72/103.23 inference(monotonicity,[status(thm)],[433])).
% 160.72/103.23 tff(435,plain,
% 160.72/103.23 (r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))),
% 160.72/103.23 inference(symmetry,[status(thm)],[434])).
% 160.72/103.23 tff(436,plain,
% 160.72/103.23 (r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))),
% 160.72/103.23 inference(modus_ponens,[status(thm)],[432, 435])).
% 160.72/103.23 tff(437,plain,
% 160.72/103.23 ((~(~((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))) <=> ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(438,plain,
% 160.72/103.23 ((r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))) <=> (~((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(439,plain,
% 160.72/103.23 ((~(r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))) <=> (~(~((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))),
% 160.72/103.23 inference(monotonicity,[status(thm)],[438])).
% 160.72/103.23 tff(440,plain,
% 160.72/103.23 ((~(r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))) <=> ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))),
% 160.72/103.23 inference(transitivity,[status(thm)],[439, 437])).
% 160.72/103.23 tff(441,plain,
% 160.72/103.23 (~(r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))),
% 160.72/103.23 inference(or_elim,[status(thm)],[135])).
% 160.72/103.23 tff(442,plain,
% 160.72/103.23 ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))),
% 160.72/103.23 inference(modus_ponens,[status(thm)],[441, 440])).
% 160.72/103.23 tff(443,plain,
% 160.72/103.23 (~r2_hidden(B!1, k18_filter_2(A!0, B!1))),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[442, 436, 432])).
% 160.72/103.23 tff(444,plain,
% 160.72/103.23 (~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))),
% 160.72/103.23 inference(modus_ponens,[status(thm)],[443, 80])).
% 160.72/103.23 tff(445,plain,
% 160.72/103.23 ((~(r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D))))) | r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))),
% 160.72/103.23 inference(tautology,[status(thm)],[])).
% 160.72/103.23 tff(446,plain,
% 160.72/103.23 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))),
% 160.72/103.23 inference(unit_resolution,[status(thm)],[445, 444, 49])).
% 160.72/103.23 tff(447,plain,
% 160.72/103.23 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(448,plain,
% 160.72/103.23 (((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | $false) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)))),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(449,plain,
% 160.72/103.23 ((B!1 = B!1) <=> $true),
% 160.72/103.23 inference(rewrite,[status(thm)],[])).
% 160.72/103.23 tff(450,plain,
% 160.72/103.23 ((~(B!1 = B!1)) <=> (~$true)),
% 160.72/103.23 inference(monotonicity,[status(thm)],[449])).
% 160.72/103.23 tff(451,plain,
% 160.72/103.23 ((~(B!1 = B!1)) <=> $false),
% 160.72/103.23 inference(transitivity,[status(thm)],[450, 416])).
% 160.72/103.23 tff(452,plain,
% 160.72/103.23 (((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | (~(B!1 = B!1))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | $false)),
% 160.72/103.23 inference(monotonicity,[status(thm)],[451])).
% 160.72/103.23 tff(453,plain,
% 160.72/103.23 (((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | (~(B!1 = B!1))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)))),
% 160.72/103.23 inference(transitivity,[status(thm)],[452, 448])).
% 160.72/103.23 tff(454,plain,
% 160.72/103.23 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | (~(B!1 = B!1)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1))))),
% 160.75/103.23 inference(monotonicity,[status(thm)],[453])).
% 160.75/103.23 tff(455,plain,
% 160.75/103.23 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | (~(B!1 = B!1)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)))),
% 160.75/103.23 inference(transitivity,[status(thm)],[454, 447])).
% 160.75/103.23 tff(456,plain,
% 160.75/103.23 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1)) | (~(B!1 = B!1)))),
% 160.75/103.23 inference(quant_inst,[status(thm)],[])).
% 160.75/103.23 tff(457,plain,
% 160.75/103.23 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(B!1 = D)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, B!1))),
% 160.75/103.23 inference(modus_ponens,[status(thm)],[456, 455])).
% 160.75/103.23 tff(458,plain,
% 160.75/103.23 (~r3_lattices(A!0, B!1, B!1)),
% 160.75/103.23 inference(unit_resolution,[status(thm)],[457, 34, 446])).
% 160.75/103.23 tff(459,plain,
% 160.75/103.23 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))),
% 160.75/103.23 inference(bind,[status(th)],[])).
% 160.75/103.23 tff(460,plain,
% 160.75/103.23 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.75/103.23 inference(quant_intro,[status(thm)],[459])).
% 160.75/103.23 tff(461,plain,
% 160.75/103.23 (^[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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & 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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | r3_lattices(A, B, B)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | r3_lattices(A, B, B)) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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)) & 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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))))),
% 160.75/103.23 inference(bind,[status(th)],[])).
% 160.75/103.23 tff(462,plain,
% 160.75/103.23 (![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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.75/103.23 inference(quant_intro,[status(thm)],[461])).
% 160.75/103.23 tff(463,plain,
% 160.75/103.23 (![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))),
% 160.75/103.23 inference(rewrite,[status(thm)],[])).
% 160.75/103.23 tff(464,plain,
% 160.75/103.23 (^[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))))),
% 160.75/103.23 inference(bind,[status(th)],[])).
% 160.75/103.23 tff(465,plain,
% 160.75/103.23 (![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))),
% 160.75/103.23 inference(quant_intro,[status(thm)],[464])).
% 160.75/103.23 tff(466,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/sandbox2/benchmark/theBenchmark.p','reflexivity_r3_lattices')).
% 160.75/103.23 tff(467,plain,
% 160.75/103.23 (![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))),
% 160.75/103.23 inference(modus_ponens,[status(thm)],[466, 465])).
% 160.75/103.23 tff(468,plain,
% 160.75/103.23 (![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))),
% 160.75/103.23 inference(modus_ponens,[status(thm)],[467, 463])).
% 160.75/103.23 tff(469,plain,(
% 160.75/103.23 ![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))),
% 160.75/103.23 inference(skolemize,[status(sab)],[468])).
% 160.75/103.23 tff(470,plain,
% 160.75/103.23 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.75/103.23 inference(modus_ponens,[status(thm)],[469, 462])).
% 160.75/103.23 tff(471,plain,
% 160.75/103.23 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 160.75/103.23 inference(modus_ponens,[status(thm)],[470, 460])).
% 160.75/103.23 tff(472,plain,
% 160.75/103.23 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), 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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))))),
% 160.75/103.24 inference(rewrite,[status(thm)],[])).
% 160.75/103.24 tff(473,plain,
% 160.75/103.24 ((v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_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)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))))),
% 160.75/103.24 inference(rewrite,[status(thm)],[])).
% 160.75/103.24 tff(474,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)))))),
% 160.75/103.24 inference(monotonicity,[status(thm)],[473])).
% 160.75/103.24 tff(475,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_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))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_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(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))))),
% 160.75/103.24 inference(transitivity,[status(thm)],[474, 472])).
% 160.75/103.24 tff(476,plain,
% 160.75/103.24 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))),
% 160.75/103.24 inference(quant_inst,[status(thm)],[])).
% 160.75/103.24 tff(477,plain,
% 160.75/103.24 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)))),
% 160.75/103.24 inference(modus_ponens,[status(thm)],[476, 475])).
% 160.75/103.24 tff(478,plain,
% 160.75/103.24 ($false),
% 160.75/103.24 inference(unit_resolution,[status(thm)],[477, 37, 35, 34, 471, 121, 243, 241, 458, 1])).
% 160.75/103.24 tff(479,plain,(~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))), inference(lemma,lemma(discharge,[]))).
% 160.75/103.24 tff(480,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))),
% 160.75/103.24 inference(rewrite,[status(thm)],[])).
% 160.75/103.24 tff(481,plain,
% 160.75/103.24 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))),
% 160.75/103.24 inference(rewrite,[status(thm)],[])).
% 160.75/103.24 tff(482,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))),
% 160.75/103.24 inference(monotonicity,[status(thm)],[481])).
% 160.75/103.24 tff(483,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))),
% 160.75/103.24 inference(transitivity,[status(thm)],[482, 480])).
% 160.75/103.24 tff(484,plain,
% 160.75/103.24 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 160.75/103.24 inference(quant_inst,[status(thm)],[])).
% 160.75/103.24 tff(485,plain,
% 160.75/103.24 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))),
% 160.75/103.24 inference(modus_ponens,[status(thm)],[484, 483])).
% 160.75/103.24 tff(486,plain,
% 160.75/103.24 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))),
% 160.75/103.24 inference(unit_resolution,[status(thm)],[485, 136, 406, 393, 391, 369, 332])).
% 160.75/103.24 tff(487,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))),
% 160.75/103.24 inference(rewrite,[status(thm)],[])).
% 160.75/103.24 tff(488,plain,
% 160.75/103.24 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))),
% 160.75/103.24 inference(rewrite,[status(thm)],[])).
% 160.75/103.24 tff(489,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))),
% 160.75/103.24 inference(monotonicity,[status(thm)],[488])).
% 160.75/103.24 tff(490,plain,
% 160.75/103.24 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))),
% 160.75/103.25 inference(transitivity,[status(thm)],[489, 487])).
% 160.75/103.25 tff(491,plain,
% 160.75/103.25 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))),
% 160.75/103.25 inference(quant_inst,[status(thm)],[])).
% 160.75/103.25 tff(492,plain,
% 160.75/103.25 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))),
% 160.75/103.25 inference(modus_ponens,[status(thm)],[491, 490])).
% 160.75/103.25 tff(493,plain,
% 160.75/103.25 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))),
% 160.75/103.25 inference(unit_resolution,[status(thm)],[492, 406, 393, 391, 369, 332, 413, 486])).
% 160.75/103.25 tff(494,plain,
% 160.75/103.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))),
% 160.75/103.25 inference(rewrite,[status(thm)],[])).
% 160.75/103.25 tff(495,plain,
% 160.75/103.25 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))),
% 160.75/103.25 inference(rewrite,[status(thm)],[])).
% 160.75/103.25 tff(496,plain,
% 160.75/103.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))))),
% 160.75/103.25 inference(monotonicity,[status(thm)],[495])).
% 160.75/103.25 tff(497,plain,
% 160.75/103.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))),
% 160.75/103.25 inference(transitivity,[status(thm)],[496, 494])).
% 160.75/103.25 tff(498,plain,
% 160.75/103.25 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))),
% 160.75/103.25 inference(quant_inst,[status(thm)],[])).
% 160.75/103.25 tff(499,plain,
% 160.75/103.25 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))),
% 160.75/103.25 inference(modus_ponens,[status(thm)],[498, 497])).
% 160.75/103.25 tff(500,plain,
% 160.75/103.25 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))),
% 160.75/103.25 inference(unit_resolution,[status(thm)],[499, 34, 406, 393, 391, 369, 332, 486])).
% 160.75/103.25 tff(501,plain,
% 160.75/103.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 160.75/103.25 inference(rewrite,[status(thm)],[])).
% 160.75/103.25 tff(502,plain,
% 160.75/103.25 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 160.75/103.25 inference(rewrite,[status(thm)],[])).
% 160.75/103.25 tff(503,plain,
% 160.75/103.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))),
% 160.75/103.25 inference(monotonicity,[status(thm)],[502])).
% 160.75/103.25 tff(504,plain,
% 160.75/103.25 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 160.75/103.26 inference(transitivity,[status(thm)],[503, 501])).
% 160.75/103.26 tff(505,plain,
% 160.75/103.26 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))),
% 160.75/103.26 inference(quant_inst,[status(thm)],[])).
% 160.75/103.26 tff(506,plain,
% 160.75/103.26 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))),
% 160.75/103.26 inference(modus_ponens,[status(thm)],[505, 504])).
% 160.75/103.26 tff(507,plain,
% 160.75/103.26 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))),
% 160.75/103.26 inference(unit_resolution,[status(thm)],[506, 406, 393, 391, 369, 332, 500, 493])).
% 160.75/103.26 tff(508,plain,
% 160.75/103.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)))),
% 160.75/103.26 inference(rewrite,[status(thm)],[])).
% 160.75/103.26 tff(509,plain,
% 160.75/103.26 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)))),
% 160.75/103.26 inference(rewrite,[status(thm)],[])).
% 160.75/103.26 tff(510,plain,
% 160.75/103.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))))),
% 160.75/103.26 inference(monotonicity,[status(thm)],[509])).
% 160.75/103.26 tff(511,plain,
% 160.75/103.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)))),
% 160.75/103.26 inference(transitivity,[status(thm)],[510, 508])).
% 160.75/103.26 tff(512,plain,
% 160.75/103.26 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))))),
% 160.75/103.26 inference(quant_inst,[status(thm)],[])).
% 160.75/103.26 tff(513,plain,
% 160.75/103.26 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))),
% 160.75/103.26 inference(modus_ponens,[status(thm)],[512, 511])).
% 160.75/103.26 tff(514,plain,
% 160.75/103.26 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))),
% 160.75/103.26 inference(unit_resolution,[status(thm)],[513, 34, 406, 393, 391, 369, 332, 500])).
% 160.75/103.26 tff(515,plain,
% 160.75/103.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)))),
% 160.75/103.26 inference(rewrite,[status(thm)],[])).
% 160.75/103.26 tff(516,plain,
% 160.75/103.26 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)))),
% 160.75/103.26 inference(rewrite,[status(thm)],[])).
% 160.75/103.26 tff(517,plain,
% 160.75/103.26 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))))),
% 160.75/103.27 inference(monotonicity,[status(thm)],[516])).
% 160.75/103.27 tff(518,plain,
% 160.75/103.27 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)))),
% 160.75/103.27 inference(transitivity,[status(thm)],[517, 515])).
% 160.75/103.27 tff(519,plain,
% 160.75/103.27 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))),
% 160.75/103.27 inference(quant_inst,[status(thm)],[])).
% 160.75/103.27 tff(520,plain,
% 160.75/103.27 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2))), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))), u1_struct_0(A!0))),
% 160.91/103.44 inference(modus_ponens,[status(thm)],[519, 518])).
% 160.91/103.44 tff(521,plain,
% 160.91/103.44 ($false),
% 160.91/103.44 inference(unit_resolution,[status(thm)],[520, 406, 393, 391, 369, 332, 514, 507, 479])).
% 160.91/103.44 % SZS output end Proof
%------------------------------------------------------------------------------