%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT289+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 Jun 21 05:14:11 AM UTC 2025
% Result : Theorem 3.66s 3.87s
% Output : Proof 3.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT289+1 : TPTP v9.0.0. Released v3.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 20:03:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.66/3.87 % SZS status Theorem
% 3.66/3.87 % SZS output start Proof
% 3.66/3.87 tff(r2_hidden_type, type, (
% 3.66/3.87 r2_hidden: ( $i * $i ) > $o)).
% 3.66/3.87 tff(k8_funct_2_type, type, (
% 3.66/3.87 k8_funct_2: ( $i * $i * $i * $i ) > $i)).
% 3.66/3.87 tff(tptp_fun_B_1_type, type, (
% 3.66/3.87 tptp_fun_B_1: $i)).
% 3.66/3.87 tff(k9_lopclset_type, type, (
% 3.66/3.87 k9_lopclset: $i > $i)).
% 3.66/3.87 tff(tptp_fun_A_0_type, type, (
% 3.66/3.87 tptp_fun_A_0: $i)).
% 3.66/3.87 tff(k1_zfmisc_1_type, type, (
% 3.66/3.87 k1_zfmisc_1: $i > $i)).
% 3.66/3.87 tff(k7_lopclset_type, type, (
% 3.66/3.87 k7_lopclset: $i > $i)).
% 3.66/3.87 tff(u1_struct_0_type, type, (
% 3.66/3.87 u1_struct_0: $i > $i)).
% 3.66/3.87 tff(tptp_fun_C_2_type, type, (
% 3.66/3.87 tptp_fun_C_2: $i)).
% 3.66/3.87 tff(k1_funct_1_type, type, (
% 3.66/3.87 k1_funct_1: ( $i * $i ) > $i)).
% 3.66/3.87 tff(k8_lopclset_type, type, (
% 3.66/3.87 k8_lopclset: $i > $i)).
% 3.66/3.87 tff(v17_lattices_type, type, (
% 3.66/3.87 v17_lattices: $i > $o)).
% 3.66/3.87 tff(v10_lattices_type, type, (
% 3.66/3.87 v10_lattices: $i > $o)).
% 3.66/3.87 tff(l3_lattices_type, type, (
% 3.66/3.87 l3_lattices: $i > $o)).
% 3.66/3.87 tff(v3_struct_0_type, type, (
% 3.66/3.87 v3_struct_0: $i > $o)).
% 3.66/3.87 tff(v3_realset2_type, type, (
% 3.66/3.87 v3_realset2: $i > $o)).
% 3.66/3.87 tff(v1_filter_0_type, type, (
% 3.66/3.87 v1_filter_0: ( $i * $i ) > $o)).
% 3.66/3.87 tff(m1_filter_0_type, type, (
% 3.66/3.87 m1_filter_0: ( $i * $i ) > $o)).
% 3.66/3.87 tff(m1_subset_1_type, type, (
% 3.66/3.87 m1_subset_1: ( $i * $i ) > $o)).
% 3.66/3.87 tff(v1_xboole_0_type, type, (
% 3.66/3.87 v1_xboole_0: $i > $o)).
% 3.66/3.87 tff(l1_struct_0_type, type, (
% 3.66/3.87 l1_struct_0: $i > $o)).
% 3.66/3.87 tff(l2_lattices_type, type, (
% 3.66/3.87 l2_lattices: $i > $o)).
% 3.66/3.87 tff(l1_lattices_type, type, (
% 3.66/3.87 l1_lattices: $i > $o)).
% 3.66/3.87 tff(v1_funct_1_type, type, (
% 3.66/3.87 v1_funct_1: $i > $o)).
% 3.66/3.87 tff(m2_relset_1_type, type, (
% 3.66/3.87 m2_relset_1: ( $i * $i * $i ) > $o)).
% 3.66/3.87 tff(v1_funct_2_type, type, (
% 3.66/3.87 v1_funct_2: ( $i * $i * $i ) > $o)).
% 3.66/3.87 tff(m1_relset_1_type, type, (
% 3.66/3.87 m1_relset_1: ( $i * $i * $i ) > $o)).
% 3.66/3.87 tff(1,plain,
% 3.66/3.87 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(2,plain,
% 3.66/3.87 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[1])).
% 3.66/3.87 tff(3,plain,
% 3.66/3.87 (^[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))) | (k9_lopclset(A) = k8_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_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))) | (k9_lopclset(A) = k8_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(4,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[3])).
% 3.66/3.87 tff(5,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(6,plain,
% 3.66/3.87 (^[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)) => (k9_lopclset(A) = k8_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(7,plain,
% 3.66/3.87 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[6])).
% 3.66/3.87 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k9_lopclset(A) = k8_lopclset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k9_lopclset')).
% 3.66/3.87 tff(9,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[8, 7])).
% 3.66/3.87 tff(10,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[9, 5])).
% 3.66/3.87 tff(11,plain,(
% 3.66/3.87 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k9_lopclset(A) = k8_lopclset(A)))),
% 3.66/3.87 inference(skolemize,[status(sab)],[10])).
% 3.66/3.87 tff(12,plain,
% 3.66/3.87 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[11, 4])).
% 3.66/3.87 tff(13,plain,
% 3.66/3.87 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[12, 2])).
% 3.66/3.87 tff(14,plain,
% 3.66/3.87 ((((~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)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))) <=> ((~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)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(15,plain,
% 3.66/3.87 ((~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))) <=> (~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C)))))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(16,plain,
% 3.66/3.87 ((~![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)) => ![C: $i] : (m1_filter_0(C, A) => (~((v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)))) & r2_hidden(B, C))))))) <=> (~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C)))))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(17,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)) => ![C: $i] : (m1_filter_0(C, A) => (~((v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B)))) & r2_hidden(B, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t27_lopclset')).
% 3.66/3.87 tff(18,plain,
% 3.66/3.87 (~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.66/3.87 tff(19,plain,
% 3.66/3.87 (~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[18, 15])).
% 3.66/3.87 tff(20,plain,
% 3.66/3.87 (~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[19, 15])).
% 3.66/3.87 tff(21,plain,
% 3.66/3.87 (~![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(v1_filter_0(C, A) & (~r2_hidden(C, k8_funct_2(u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)), k9_lopclset(A), B))) & r2_hidden(B, C))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[20, 15])).
% 3.66/3.87 tff(22,plain,
% 3.66/3.87 ((~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)) & (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2)))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.66/3.87 tff(23,plain,
% 3.66/3.87 (l3_lattices(A!0)),
% 3.66/3.87 inference(and_elim,[status(thm)],[22])).
% 3.66/3.87 tff(24,plain,
% 3.66/3.87 (~v3_realset2(A!0)),
% 3.66/3.87 inference(and_elim,[status(thm)],[22])).
% 3.66/3.87 tff(25,plain,
% 3.66/3.87 (v17_lattices(A!0)),
% 3.66/3.87 inference(and_elim,[status(thm)],[22])).
% 3.66/3.87 tff(26,plain,
% 3.66/3.87 (v10_lattices(A!0)),
% 3.66/3.87 inference(and_elim,[status(thm)],[22])).
% 3.66/3.87 tff(27,plain,
% 3.66/3.87 (~v3_struct_0(A!0)),
% 3.66/3.87 inference(and_elim,[status(thm)],[22])).
% 3.66/3.87 tff(28,plain,
% 3.66/3.87 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~v17_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~v17_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(29,plain,
% 3.66/3.87 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~v17_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(30,plain,
% 3.66/3.87 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~v17_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0))))),
% 3.66/3.87 inference(monotonicity,[status(thm)],[29])).
% 3.66/3.87 tff(31,plain,
% 3.66/3.87 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~v17_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0)))),
% 3.66/3.87 inference(transitivity,[status(thm)],[30, 28])).
% 3.66/3.87 tff(32,plain,
% 3.66/3.87 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k9_lopclset(A!0) = k8_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 3.66/3.87 inference(quant_inst,[status(thm)],[])).
% 3.66/3.87 tff(33,plain,
% 3.66/3.87 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k9_lopclset(A) = k8_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~v17_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k9_lopclset(A!0) = k8_lopclset(A!0))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[32, 31])).
% 3.66/3.87 tff(34,plain,
% 3.66/3.87 (k9_lopclset(A!0) = k8_lopclset(A!0)),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 3.66/3.87 tff(35,plain,
% 3.66/3.87 (k8_lopclset(A!0) = k9_lopclset(A!0)),
% 3.66/3.87 inference(symmetry,[status(thm)],[34])).
% 3.66/3.87 tff(36,plain,
% 3.66/3.87 (k1_funct_1(k8_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)),
% 3.66/3.87 inference(monotonicity,[status(thm)],[35])).
% 3.66/3.87 tff(37,plain,
% 3.66/3.87 (k1_funct_1(k9_lopclset(A!0), B!1) = k1_funct_1(k8_lopclset(A!0), B!1)),
% 3.66/3.87 inference(symmetry,[status(thm)],[36])).
% 3.66/3.87 tff(38,plain,
% 3.66/3.87 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(39,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[38])).
% 3.66/3.87 tff(40,plain,
% 3.66/3.87 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(41,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[40])).
% 3.66/3.87 tff(42,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(43,plain,
% 3.66/3.87 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(44,plain,
% 3.66/3.87 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[43])).
% 3.66/3.87 tff(45,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 3.66/3.87 tff(46,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[45, 44])).
% 3.66/3.87 tff(47,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[46, 42])).
% 3.66/3.87 tff(48,plain,(
% 3.66/3.87 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.66/3.87 inference(skolemize,[status(sab)],[47])).
% 3.66/3.87 tff(49,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[48, 41])).
% 3.66/3.87 tff(50,plain,
% 3.66/3.87 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[49, 39])).
% 3.66/3.87 tff(51,plain,
% 3.66/3.87 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(52,plain,
% 3.66/3.87 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 3.66/3.87 inference(quant_inst,[status(thm)],[])).
% 3.66/3.87 tff(53,plain,
% 3.66/3.87 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[52, 51])).
% 3.66/3.87 tff(54,plain,
% 3.66/3.87 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[53, 23, 50])).
% 3.66/3.87 tff(55,plain,
% 3.66/3.87 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 3.66/3.87 inference(tautology,[status(thm)],[])).
% 3.66/3.87 tff(56,plain,
% 3.66/3.87 (l2_lattices(A!0)),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[55, 54])).
% 3.66/3.87 tff(57,plain,
% 3.66/3.87 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(58,plain,
% 3.66/3.87 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[57])).
% 3.66/3.87 tff(59,plain,
% 3.66/3.87 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(60,plain,
% 3.66/3.87 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(61,plain,
% 3.66/3.87 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[60])).
% 3.66/3.87 tff(62,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 3.66/3.87 tff(63,plain,
% 3.66/3.87 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[62, 61])).
% 3.66/3.87 tff(64,plain,
% 3.66/3.87 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[63, 59])).
% 3.66/3.87 tff(65,plain,(
% 3.66/3.87 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(skolemize,[status(sab)],[64])).
% 3.66/3.87 tff(66,plain,
% 3.66/3.87 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[65, 58])).
% 3.66/3.87 tff(67,plain,
% 3.66/3.87 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(68,plain,
% 3.66/3.87 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 3.66/3.87 inference(quant_inst,[status(thm)],[])).
% 3.66/3.87 tff(69,plain,
% 3.66/3.87 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.66/3.87 tff(70,plain,
% 3.66/3.87 (l1_struct_0(A!0)),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[69, 66, 56])).
% 3.66/3.87 tff(71,plain,
% 3.66/3.87 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(72,plain,
% 3.66/3.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[71])).
% 3.66/3.87 tff(73,plain,
% 3.66/3.87 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(74,plain,
% 3.66/3.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[73])).
% 3.66/3.87 tff(75,plain,
% 3.66/3.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(76,plain,
% 3.66/3.87 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(77,plain,
% 3.66/3.87 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[76])).
% 3.66/3.87 tff(78,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 3.66/3.87 tff(79,plain,
% 3.66/3.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[78, 77])).
% 3.66/3.87 tff(80,plain,
% 3.66/3.87 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[79, 75])).
% 3.66/3.87 tff(81,plain,(
% 3.66/3.87 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.66/3.87 inference(skolemize,[status(sab)],[80])).
% 3.66/3.87 tff(82,plain,
% 3.66/3.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[81, 74])).
% 3.66/3.87 tff(83,plain,
% 3.66/3.87 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[82, 72])).
% 3.66/3.87 tff(84,plain,
% 3.66/3.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(85,plain,
% 3.66/3.87 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(86,plain,
% 3.66/3.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 3.66/3.87 inference(monotonicity,[status(thm)],[85])).
% 3.66/3.87 tff(87,plain,
% 3.66/3.87 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 3.66/3.87 inference(transitivity,[status(thm)],[86, 84])).
% 3.66/3.87 tff(88,plain,
% 3.66/3.87 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 3.66/3.87 inference(quant_inst,[status(thm)],[])).
% 3.66/3.87 tff(89,plain,
% 3.66/3.87 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[88, 87])).
% 3.66/3.87 tff(90,plain,
% 3.66/3.87 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[89, 27, 83])).
% 3.66/3.87 tff(91,plain,
% 3.66/3.87 (~v1_xboole_0(u1_struct_0(A!0))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[90, 70])).
% 3.66/3.87 tff(92,plain,
% 3.66/3.87 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(93,plain,
% 3.66/3.87 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[92])).
% 3.66/3.87 tff(94,plain,
% 3.66/3.87 (^[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))))), rewrite((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) <=> (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(95,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[94])).
% 3.66/3.87 tff(96,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(97,plain,
% 3.66/3.87 (^[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)))), rewrite(((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) <=> (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(98,plain,
% 3.66/3.87 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[97])).
% 3.66/3.87 tff(99,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k9_lopclset')).
% 3.66/3.87 tff(100,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[99, 98])).
% 3.66/3.87 tff(101,plain,
% 3.66/3.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[100, 96])).
% 3.66/3.87 tff(102,plain,(
% 3.66/3.87 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_funct_1(k9_lopclset(A)) & v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A))) & m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))),
% 3.66/3.87 inference(skolemize,[status(sab)],[101])).
% 3.66/3.87 tff(103,plain,
% 3.66/3.87 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[102, 95])).
% 3.66/3.87 tff(104,plain,
% 3.66/3.87 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[103, 93])).
% 3.66/3.87 tff(105,plain,
% 3.66/3.87 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(106,plain,
% 3.66/3.87 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))))),
% 3.66/3.87 inference(quant_inst,[status(thm)],[])).
% 3.66/3.87 tff(107,plain,
% 3.66/3.87 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_funct_1(k9_lopclset(A))) | (~v1_funct_2(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))) | (~m2_relset_1(k9_lopclset(A), u1_struct_0(A), k1_zfmisc_1(k7_lopclset(A)))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[106, 105])).
% 3.66/3.87 tff(108,plain,
% 3.66/3.87 (~((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[107, 27, 26, 25, 24, 23, 104])).
% 3.66/3.87 tff(109,plain,
% 3.66/3.87 (((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | v1_funct_1(k9_lopclset(A!0))),
% 3.66/3.87 inference(tautology,[status(thm)],[])).
% 3.66/3.87 tff(110,plain,
% 3.66/3.87 (v1_funct_1(k9_lopclset(A!0))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[109, 108])).
% 3.66/3.87 tff(111,plain,
% 3.66/3.87 (((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(tautology,[status(thm)],[])).
% 3.66/3.87 tff(112,plain,
% 3.66/3.87 (v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[111, 108])).
% 3.66/3.87 tff(113,plain,
% 3.66/3.87 (m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(monotonicity,[status(thm)],[35])).
% 3.66/3.87 tff(114,plain,
% 3.66/3.87 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(115,plain,
% 3.66/3.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[114])).
% 3.66/3.87 tff(116,plain,
% 3.66/3.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.66/3.87 inference(rewrite,[status(thm)],[])).
% 3.66/3.87 tff(117,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 3.66/3.87 tff(118,plain,
% 3.66/3.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[117, 116])).
% 3.66/3.87 tff(119,plain,(
% 3.66/3.87 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.66/3.87 inference(skolemize,[status(sab)],[118])).
% 3.66/3.87 tff(120,plain,
% 3.66/3.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[119, 115])).
% 3.66/3.87 tff(121,plain,
% 3.66/3.87 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))),
% 3.66/3.87 inference(quant_inst,[status(thm)],[])).
% 3.66/3.87 tff(122,plain,
% 3.66/3.87 (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[121, 120])).
% 3.66/3.87 tff(123,plain,
% 3.66/3.87 (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(monotonicity,[status(thm)],[35])).
% 3.66/3.87 tff(124,plain,
% 3.66/3.87 (m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(symmetry,[status(thm)],[123])).
% 3.66/3.87 tff(125,plain,
% 3.66/3.87 (((~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(tautology,[status(thm)],[])).
% 3.66/3.87 tff(126,plain,
% 3.66/3.87 (m2_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[125, 108])).
% 3.66/3.87 tff(127,plain,
% 3.66/3.87 (m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[126, 124])).
% 3.66/3.87 tff(128,plain,
% 3.66/3.87 ((~(m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))) <=> m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))) | (~m2_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(tautology,[status(thm)],[])).
% 3.66/3.87 tff(129,plain,
% 3.66/3.87 (m1_relset_1(k8_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(unit_resolution,[status(thm)],[128, 127, 122])).
% 3.66/3.87 tff(130,plain,
% 3.66/3.87 (m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))),
% 3.66/3.87 inference(modus_ponens,[status(thm)],[129, 113])).
% 3.66/3.87 tff(131,plain,
% 3.66/3.87 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))),
% 3.66/3.87 inference(bind,[status(th)],[])).
% 3.66/3.87 tff(132,plain,
% 3.66/3.87 (![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 3.66/3.87 inference(quant_intro,[status(thm)],[131])).
% 3.66/3.87 tff(133,plain,
% 3.66/3.87 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) <=> (~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))))), rewrite((~(~(v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) <=> (v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite(((v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))), (((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))))),
% 3.66/3.88 inference(bind,[status(th)],[])).
% 3.66/3.88 tff(134,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 3.66/3.88 inference(quant_intro,[status(thm)],[133])).
% 3.66/3.88 tff(135,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 3.66/3.88 inference(rewrite,[status(thm)],[])).
% 3.66/3.88 tff(136,plain,
% 3.66/3.88 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), (((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))), ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) <=> ((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> (((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))))), rewrite((((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), (((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))))),
% 3.66/3.88 inference(bind,[status(th)],[])).
% 3.66/3.88 tff(137,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 3.66/3.88 inference(quant_intro,[status(thm)],[136])).
% 3.66/3.88 tff(138,axiom,(![A: $i, B: $i, C: $i, D: $i] : ((((((~v1_xboole_0(A)) & v1_funct_1(C)) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) & m1_subset_1(D, A)) => (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k8_funct_2')).
% 3.66/3.88 tff(139,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 3.66/3.88 inference(modus_ponens,[status(thm)],[138, 137])).
% 3.66/3.88 tff(140,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 3.66/3.88 inference(modus_ponens,[status(thm)],[139, 135])).
% 3.66/3.88 tff(141,plain,(
% 3.66/3.88 ![A: $i, B: $i, C: $i, D: $i] : ((~((~v1_xboole_0(A)) & v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B) & m1_subset_1(D, A))) | (k8_funct_2(A, B, C, D) = k1_funct_1(C, D)))),
% 3.66/3.88 inference(skolemize,[status(sab)],[140])).
% 3.66/3.88 tff(142,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 3.66/3.88 inference(modus_ponens,[status(thm)],[141, 134])).
% 3.66/3.88 tff(143,plain,
% 3.66/3.88 (![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))),
% 3.66/3.88 inference(modus_ponens,[status(thm)],[142, 132])).
% 3.66/3.88 tff(144,plain,
% 3.66/3.88 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 3.66/3.88 inference(and_elim,[status(thm)],[22])).
% 3.66/3.88 tff(145,plain,
% 3.66/3.88 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 3.66/3.88 inference(rewrite,[status(thm)],[])).
% 3.66/3.88 tff(146,plain,
% 3.66/3.88 (((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 3.66/3.88 inference(rewrite,[status(thm)],[])).
% 3.66/3.88 tff(147,plain,
% 3.66/3.88 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))))),
% 3.66/3.88 inference(monotonicity,[status(thm)],[146])).
% 3.66/3.88 tff(148,plain,
% 3.66/3.88 (((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))))),
% 3.66/3.88 inference(transitivity,[status(thm)],[147, 145])).
% 3.66/3.88 tff(149,plain,
% 3.66/3.88 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | ((k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 3.66/3.88 inference(quant_inst,[status(thm)],[])).
% 3.66/3.88 tff(150,plain,
% 3.66/3.88 ((~![A: $i, B: $i, C: $i, D: $i] : ((k8_funct_2(A, B, C, D) = k1_funct_1(C, D)) | v1_xboole_0(A) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)) | (~m1_subset_1(D, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))),
% 3.66/3.88 inference(modus_ponens,[status(thm)],[149, 148])).
% 3.66/3.88 tff(151,plain,
% 3.66/3.88 (v1_xboole_0(u1_struct_0(A!0)) | (~v1_funct_1(k9_lopclset(A!0))) | (~v1_funct_2(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)))) | (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)) | (~m1_relset_1(k9_lopclset(A!0), u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0))))),
% 3.66/3.88 inference(unit_resolution,[status(thm)],[150, 144, 143])).
% 3.66/3.88 tff(152,plain,
% 3.66/3.88 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k9_lopclset(A!0), B!1)),
% 3.66/3.88 inference(unit_resolution,[status(thm)],[151, 130, 112, 110, 91])).
% 3.66/3.88 tff(153,plain,
% 3.66/3.88 (k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1) = k1_funct_1(k8_lopclset(A!0), B!1)),
% 3.66/3.88 inference(transitivity,[status(thm)],[152, 37])).
% 3.66/3.88 tff(154,plain,
% 3.66/3.88 (r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1)) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 3.66/3.88 inference(monotonicity,[status(thm)],[153])).
% 3.66/3.88 tff(155,plain,
% 3.66/3.88 (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)) <=> r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))),
% 3.66/3.88 inference(symmetry,[status(thm)],[154])).
% 3.66/3.88 tff(156,plain,
% 3.66/3.88 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))))),
% 3.66/3.88 inference(bind,[status(th)],[])).
% 3.66/3.88 tff(157,plain,
% 3.66/3.88 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))),
% 3.66/3.88 inference(quant_intro,[status(thm)],[156])).
% 3.66/3.88 tff(158,plain,
% 3.66/3.88 (^[A: $i] : rewrite((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))))),
% 3.66/3.88 inference(bind,[status(th)],[])).
% 3.66/3.88 tff(159,plain,
% 3.66/3.88 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))),
% 3.66/3.88 inference(quant_intro,[status(thm)],[158])).
% 3.66/3.88 tff(160,plain,
% 3.66/3.88 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))),
% 3.66/3.88 inference(transitivity,[status(thm)],[159, 157])).
% 3.66/3.88 tff(161,plain,
% 3.66/3.88 (^[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))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))), (((~((~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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B))))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))), (((~((~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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))))),
% 3.66/3.88 inference(bind,[status(th)],[])).
% 3.66/3.88 tff(162,plain,
% 3.66/3.88 (![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))),
% 3.66/3.88 inference(quant_intro,[status(thm)],[161])).
% 3.66/3.88 tff(163,plain,
% 3.66/3.88 (![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 3.66/3.88 inference(rewrite,[status(thm)],[])).
% 3.66/3.88 tff(164,plain,
% 3.66/3.88 (^[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)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))) <=> ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))), (![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))) <=> ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), (((((((~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)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> (((~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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))))), rewrite((((~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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ((~((~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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), (((((((~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)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ((~((~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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))))),
% 3.66/3.88 inference(bind,[status(th)],[])).
% 3.66/3.88 tff(165,plain,
% 3.66/3.88 (![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)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C)))))) <=> ![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 3.66/3.88 inference(quant_intro,[status(thm)],[164])).
% 3.66/3.88 tff(166,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)) => ![C: $i] : (m1_filter_0(C, A) => (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t21_lopclset')).
% 3.66/3.88 tff(167,plain,
% 3.66/3.88 (![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[166, 165])).
% 3.72/3.88 tff(168,plain,
% 3.72/3.88 (![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[167, 163])).
% 3.72/3.88 tff(169,plain,(
% 3.72/3.88 ![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))) | ![C: $i] : ((~m1_filter_0(C, A)) | (r2_hidden(C, k1_funct_1(k8_lopclset(A), B)) <=> (v1_filter_0(C, A) & r2_hidden(B, C))))))),
% 3.72/3.88 inference(skolemize,[status(sab)],[168])).
% 3.72/3.88 tff(170,plain,
% 3.72/3.88 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[169, 162])).
% 3.72/3.88 tff(171,plain,
% 3.72/3.88 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[170, 160])).
% 3.72/3.88 tff(172,plain,
% 3.72/3.88 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)))))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(173,plain,
% 3.72/3.88 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B)))))))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(174,plain,
% 3.72/3.88 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_filter_0(C, A)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A), B)))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B))))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[173, 172])).
% 3.72/3.88 tff(175,plain,
% 3.72/3.88 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B))))))),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[174, 27, 26, 25, 24, 23, 171])).
% 3.72/3.88 tff(176,plain,
% 3.72/3.88 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1))))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(177,plain,
% 3.72/3.88 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1))))))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(178,plain,
% 3.72/3.88 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[177, 176])).
% 3.72/3.88 tff(179,plain,
% 3.72/3.88 (![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)))))),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[178, 144, 175])).
% 3.72/3.88 tff(180,plain,
% 3.72/3.88 (~((~m1_filter_0(C!2, A!0)) | (~(v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2))))),
% 3.72/3.88 inference(and_elim,[status(thm)],[22])).
% 3.72/3.88 tff(181,plain,
% 3.72/3.88 (m1_filter_0(C!2, A!0)),
% 3.72/3.88 inference(or_elim,[status(thm)],[180])).
% 3.72/3.88 tff(182,plain,
% 3.72/3.88 (((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)))))) | ((~m1_filter_0(C!2, A!0)) | (~(((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)))))) <=> ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)))))) | (~m1_filter_0(C!2, A!0)) | (~(((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(183,plain,
% 3.72/3.88 ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)))))) | ((~m1_filter_0(C!2, A!0)) | (~(((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)))))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(184,plain,
% 3.72/3.88 ((~![C: $i] : ((~m1_filter_0(C, A!0)) | (~(((~r2_hidden(B!1, C)) | (~v1_filter_0(C, A!0))) <=> r2_hidden(C, k1_funct_1(k8_lopclset(A!0), B!1)))))) | (~m1_filter_0(C!2, A!0)) | (~(((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[183, 182])).
% 3.72/3.88 tff(185,plain,
% 3.72/3.88 (~(((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1)))),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[184, 181, 179])).
% 3.72/3.90 tff(186,plain,
% 3.72/3.90 (v1_filter_0(C!2, A!0) & (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))) & r2_hidden(B!1, C!2)),
% 3.72/3.90 inference(or_elim,[status(thm)],[180])).
% 3.72/3.90 tff(187,plain,
% 3.72/3.90 (r2_hidden(B!1, C!2)),
% 3.72/3.90 inference(and_elim,[status(thm)],[186])).
% 3.72/3.90 tff(188,plain,
% 3.72/3.90 (v1_filter_0(C!2, A!0)),
% 3.72/3.90 inference(and_elim,[status(thm)],[186])).
% 3.72/3.90 tff(189,plain,
% 3.72/3.90 ((~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))) | (~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))),
% 3.72/3.90 inference(tautology,[status(thm)],[])).
% 3.72/3.90 tff(190,plain,
% 3.72/3.90 (~((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0)))),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[189, 188, 187])).
% 3.72/3.90 tff(191,plain,
% 3.72/3.90 ((((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))) | ((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) | r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 3.72/3.90 inference(tautology,[status(thm)],[])).
% 3.72/3.90 tff(192,plain,
% 3.72/3.90 ((((~r2_hidden(B!1, C!2)) | (~v1_filter_0(C!2, A!0))) <=> r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))) | r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[191, 190])).
% 3.72/3.90 tff(193,plain,
% 3.72/3.90 (r2_hidden(C!2, k1_funct_1(k8_lopclset(A!0), B!1))),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[192, 185])).
% 3.72/3.90 tff(194,plain,
% 3.72/3.90 (r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[193, 155])).
% 3.72/3.90 tff(195,plain,
% 3.72/3.90 (~r2_hidden(C!2, k8_funct_2(u1_struct_0(A!0), k1_zfmisc_1(k7_lopclset(A!0)), k9_lopclset(A!0), B!1))),
% 3.72/3.90 inference(and_elim,[status(thm)],[186])).
% 3.72/3.90 tff(196,plain,
% 3.72/3.90 ($false),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[195, 194])).
% 3.72/3.90 % SZS output end Proof
% 3.72/3.91 % E exiting
%------------------------------------------------------------------------------