TSTP Solution File: LAT288+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT288+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 18:32:42 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT288+1 : TPTP v8.1.0. Released v3.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 13:11:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(v1_filter_0_type, type, (
% 0.20/0.45 v1_filter_0: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_A_0_type, type, (
% 0.20/0.45 tptp_fun_A_0: $i)).
% 0.20/0.45 tff(tptp_fun_D_10_type, type, (
% 0.20/0.45 tptp_fun_D_10: ( $i * $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_C_2_type, type, (
% 0.20/0.45 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.45 tff(a_2_0_lopclset_type, type, (
% 0.20/0.45 a_2_0_lopclset: ( $i * $i ) > $i)).
% 0.20/0.45 tff(tptp_fun_B_1_type, type, (
% 0.20/0.45 tptp_fun_B_1: $i)).
% 0.20/0.45 tff(k7_lopclset_type, type, (
% 0.20/0.45 k7_lopclset: $i > $i)).
% 0.20/0.45 tff(r2_hidden_type, type, (
% 0.20/0.45 r2_hidden: ( $i * $i ) > $o)).
% 0.20/0.45 tff(m1_filter_0_type, type, (
% 0.20/0.45 m1_filter_0: ( $i * $i ) > $o)).
% 0.20/0.45 tff(l3_lattices_type, type, (
% 0.20/0.45 l3_lattices: $i > $o)).
% 0.20/0.45 tff(v17_lattices_type, type, (
% 0.20/0.45 v17_lattices: $i > $o)).
% 0.20/0.45 tff(v10_lattices_type, type, (
% 0.20/0.45 v10_lattices: $i > $o)).
% 0.20/0.45 tff(m1_subset_1_type, type, (
% 0.20/0.45 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.45 tff(u1_struct_0_type, type, (
% 0.20/0.45 u1_struct_0: $i > $i)).
% 0.20/0.45 tff(v3_struct_0_type, type, (
% 0.20/0.45 v3_struct_0: $i > $o)).
% 0.20/0.45 tff(v3_realset2_type, type, (
% 0.20/0.45 v3_realset2: $i > $o)).
% 0.20/0.45 tff(r1_tarski_type, type, (
% 0.20/0.45 r1_tarski: ( $i * $i ) > $o)).
% 0.20/0.45 tff(a_1_1_lopclset_type, type, (
% 0.20/0.45 a_1_1_lopclset: $i > $i)).
% 0.20/0.45 tff(tptp_fun_C_9_type, type, (
% 0.20/0.45 tptp_fun_C_9: ( $i * $i ) > $i)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : refl((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : rewrite((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.45 tff(6,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) <=> (~(v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (~(~(v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))))), rewrite((~(~(v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))))), trans(monotonicity(rewrite(((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) <=> ((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))), rewrite((r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))) <=> (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))), ((((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))) <=> (((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A)))))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))), rewrite((((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A)))))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))) <=> (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))), ((((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))) <=> (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))))) <=> ((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))))), rewrite(((v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B))) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B)))))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))))) <=> ![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.45 tff(8,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))))), rewrite((r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D))) <=> (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))), ((((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))), ((((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.45 tff(11,axiom,(![A: $i, B: $i, C: $i] : (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (((m1_filter_0(D, B) & (A = D)) & v1_filter_0(D, B)) & r2_hidden(C, D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_2_0_lopclset')).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_lopclset(B, C)) <=> ?[D: $i] : (m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.46 tff(14,plain,(
% 0.20/0.46 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_lopclset(B, C))) | (m1_filter_0(tptp_fun_D_10(C, B, A), B) & (A = tptp_fun_D_10(C, B, A)) & v1_filter_0(tptp_fun_D_10(C, B, A), B) & r2_hidden(C, tptp_fun_D_10(C, B, A)))) & (r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : (~(m1_filter_0(D, B) & (A = D) & v1_filter_0(D, B) & r2_hidden(C, D))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[13])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)))) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.46 tff(21,plain,
% 0.20/0.46 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(22,plain,
% 0.20/0.46 ((~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(23,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_lopclset')).
% 0.20/0.46 tff(24,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.46 tff(25,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.46 tff(26,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.46 tff(27,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.46 tff(28,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.46 tff(29,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.46 tff(30,plain,
% 0.20/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r1_tarski(a_2_0_lopclset(A, B), k7_lopclset(A))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.46 tff(31,plain,
% 0.20/0.46 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.46 tff(32,plain,
% 0.20/0.46 (~((~m1_subset_1(B!1, u1_struct_0(A!0))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(33,plain,
% 0.20/0.46 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.20/0.46 inference(or_elim,[status(thm)],[32])).
% 0.20/0.46 tff(34,plain,
% 0.20/0.46 (l3_lattices(A!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(35,plain,
% 0.20/0.46 (~v3_realset2(A!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (v17_lattices(A!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (v10_lattices(A!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (~v3_struct_0(A!0)),
% 0.20/0.46 inference(and_elim,[status(thm)],[31])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | (v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 ((v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D)))))))) <=> (v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 ((~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~r2_hidden(B!1, D)) | (~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0))))))) <=> (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(42,plain,
% 0.20/0.46 ((v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~r2_hidden(B!1, D)) | (~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)))))))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[41])).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 ((v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~r2_hidden(B!1, D)) | (~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)))))))) <=> (v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~r2_hidden(B!1, D)) | (~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | (v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D)))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.46 tff(45,plain,
% 0.20/0.46 (((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~r2_hidden(B!1, D)) | (~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[44, 39])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~r2_hidden(B!1, D)) | (~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 ((~![A: $i, B: $i, C: $i] : (v3_realset2(B) | v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_lopclset(B, C))) | (~((~m1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~(A = tptp_fun_D_10(C, B, A))) | (~v1_filter_0(tptp_fun_D_10(C, B, A), B)) | (~r2_hidden(C, tptp_fun_D_10(C, B, A))))))) | (~(r2_hidden(A, a_2_0_lopclset(B, C)) | ![D: $i] : ((~r2_hidden(C, D)) | (~m1_filter_0(D, B)) | (~(A = D)) | (~v1_filter_0(D, B))))))))) | v3_realset2(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[47, 38, 37, 36, 35, 34, 33, 16])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1)) | ![D: $i] : ((~m1_filter_0(D, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = D)) | (~v1_filter_0(D, A!0)) | (~r2_hidden(B!1, D)))))) | ((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 ((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite((~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))), rewrite((r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))) <=> (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))))), rewrite((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))), ((((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite((r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B))) <=> ![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.47 tff(61,axiom,(![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : (r2_hidden(C, A) => r2_hidden(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (![A: $i, B: $i] : (r1_tarski(A, B) <=> ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.47 tff(64,plain,(
% 0.20/0.47 ![A: $i, B: $i] : (((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B))) & (r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[63])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : (~((~((~r1_tarski(A, B)) | ![C: $i] : ((~r2_hidden(C, A)) | r2_hidden(C, B)))) | (~(r1_tarski(A, B) | (~((~r2_hidden(tptp_fun_C_2(B, A), A)) | r2_hidden(tptp_fun_C_2(B, A), B)))))))) | (~((~((~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_lopclset(A!0, B!1))) | r2_hidden(C, k7_lopclset(A!0))))) | (~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (~((~((~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_lopclset(A!0, B!1))) | r2_hidden(C, k7_lopclset(A!0))))) | (~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (((~((~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))) | ![C: $i] : ((~r2_hidden(C, a_2_0_lopclset(A!0, B!1))) | r2_hidden(C, k7_lopclset(A!0))))) | (~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))))) | (r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (~r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0))),
% 0.20/0.47 inference(or_elim,[status(thm)],[32])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 ((~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))) | r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 ((~(r1_tarski(a_2_0_lopclset(A!0, B!1), k7_lopclset(A!0)) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))))) | (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[73, 70])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 ((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 ((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))))) | (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (~((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[78, 50])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))) | v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 (v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 (((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))) | (tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[82, 79])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~r2_hidden(B!1, tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)))))) | m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[84, 79])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (^[A: $i, B: $i] : refl((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))) <=> ![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (^[A: $i, B: $i] : rewrite((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))) <=> ![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))) <=> ![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) <=> (~(v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) <=> (~(~(v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))))), rewrite((~(~(v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))))), trans(monotonicity(rewrite(((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) <=> ((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))), rewrite((r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))) <=> (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))), ((((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))) <=> (((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B))))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))), rewrite((((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B))))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))) <=> (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))), ((((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))) <=> (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))))) <=> ((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))))), rewrite(((v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B))) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B)))))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))))) <=> (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))))) <=> ![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)))), rewrite((r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B))) <=> (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.48 tff(96,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & (~v3_realset2(B))) & l3_lattices(B)) => (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : ((m1_filter_0(C, B) & (A = C)) & v1_filter_0(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fraenkel_a_1_1_lopclset')).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (r2_hidden(A, a_1_1_lopclset(B)) <=> ?[C: $i] : (m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.20/0.48 tff(99,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & (~v3_realset2(B)) & l3_lattices(B))) | (((~r2_hidden(A, a_1_1_lopclset(B))) | (m1_filter_0(tptp_fun_C_9(B, A), B) & (A = tptp_fun_C_9(B, A)) & v1_filter_0(tptp_fun_C_9(B, A), B))) & (r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : (~(m1_filter_0(C, B) & (A = C) & v1_filter_0(C, B))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[98])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | (~((~m1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0))))))))) <=> ((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | (~((~m1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0))))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | (~((~m1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (v3_realset2(B) | v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v17_lattices(B)) | (~((~((~r2_hidden(A, a_1_1_lopclset(B))) | (~((~m1_filter_0(tptp_fun_C_9(B, A), B)) | (~(A = tptp_fun_C_9(B, A))) | (~v1_filter_0(tptp_fun_C_9(B, A), B)))))) | (~(r2_hidden(A, a_1_1_lopclset(B)) | ![C: $i] : ((~m1_filter_0(C, B)) | (~(A = C)) | (~v1_filter_0(C, B))))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | (~((~m1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (~((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | (~((~m1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[104, 38, 37, 36, 35, 34, 101])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (((~((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))) | (~((~m1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_C_9(A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))))) | (~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))))) | (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.48 tff(115,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k7_lopclset(A) = a_1_1_lopclset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_lopclset')).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.20/0.48 tff(118,plain,(
% 0.20/0.48 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k7_lopclset(A) = a_1_1_lopclset(A)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[117])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[119, 109])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[122])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[123, 121])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k7_lopclset(A) = a_1_1_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k7_lopclset(A!0) = a_1_1_lopclset(A!0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.48 tff(127,plain,
% 0.20/0.48 (k7_lopclset(A!0) = a_1_1_lopclset(A!0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[126, 38, 37, 36, 35, 34, 120])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (a_1_1_lopclset(A!0) = k7_lopclset(A!0)),
% 0.20/0.48 inference(symmetry,[status(thm)],[127])).
% 0.20/0.48 tff(129,plain,
% 0.20/0.48 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)) <=> r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))),
% 0.20/0.48 inference(symmetry,[status(thm)],[129])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 ((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))) <=> (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 (((~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_2_0_lopclset(A!0, B!1))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))) | (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), k7_lopclset(A!0))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[132, 74])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (~r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 ((~(r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0))))) | r2_hidden(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)), a_1_1_lopclset(A!0)) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[135, 134, 107])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))) | ((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))) <=> ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))) | (~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))) | ((~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = C)) | (~v1_filter_0(C, A!0)))) | (~m1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0)) | (~(tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1)) = tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))))) | (~v1_filter_0(tptp_fun_D_10(B!1, A!0, tptp_fun_C_2(k7_lopclset(A!0), a_2_0_lopclset(A!0, B!1))), A!0))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[139, 136, 85, 83, 81])).
% 0.20/0.49 % SZS output end Proof
%------------------------------------------------------------------------------