%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT286+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:14:10 AM UTC 2025
% Result : Theorem 120.52s 120.69s
% Output : Proof 121.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT286+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 20:00:24 EDT 2025
% 0.13/0.34 % CPUTime :
% 120.52/120.69 % SZS status Theorem
% 120.52/120.69 % SZS output start Proof
% 120.52/120.69 tff(r2_hidden_type, type, (
% 120.52/120.69 r2_hidden: ( $i * $i ) > $o)).
% 120.52/120.69 tff(a_1_0_lopclset_type, type, (
% 120.52/120.69 a_1_0_lopclset: $i > $i)).
% 120.52/120.69 tff(tptp_fun_A_0_type, type, (
% 120.52/120.69 tptp_fun_A_0: $i)).
% 120.52/120.69 tff(k2_pre_topc_type, type, (
% 120.52/120.69 k2_pre_topc: $i > $i)).
% 120.52/120.69 tff(u1_struct_0_type, type, (
% 120.52/120.69 u1_struct_0: $i > $i)).
% 120.52/120.69 tff(k6_lopclset_type, type, (
% 120.52/120.69 k6_lopclset: $i > $i)).
% 120.52/120.69 tff(u1_lattices_type, type, (
% 120.52/120.69 u1_lattices: $i > $i)).
% 120.52/120.69 tff(k5_lopclset_type, type, (
% 120.52/120.69 k5_lopclset: $i > $i)).
% 120.52/120.69 tff(u2_lattices_type, type, (
% 120.52/120.69 u2_lattices: $i > $i)).
% 120.52/120.69 tff(k4_lopclset_type, type, (
% 120.52/120.69 k4_lopclset: $i > $i)).
% 120.52/120.69 tff(g3_lattices_type, type, (
% 120.52/120.69 g3_lattices: ( $i * $i * $i ) > $i)).
% 120.52/120.69 tff(l3_lattices_type, type, (
% 120.52/120.69 l3_lattices: $i > $o)).
% 120.52/120.69 tff(v10_lattices_type, type, (
% 120.52/120.69 v10_lattices: $i > $o)).
% 120.52/120.69 tff(v3_struct_0_type, type, (
% 120.52/120.69 v3_struct_0: $i > $o)).
% 120.52/120.69 tff(v2_pre_topc_type, type, (
% 120.52/120.69 v2_pre_topc: $i > $o)).
% 120.52/120.69 tff(l1_pre_topc_type, type, (
% 120.52/120.69 l1_pre_topc: $i > $o)).
% 120.52/120.69 tff(m1_subset_1_type, type, (
% 120.52/120.69 m1_subset_1: ( $i * $i ) > $o)).
% 120.52/120.69 tff(v3_lattices_type, type, (
% 120.52/120.69 v3_lattices: $i > $o)).
% 120.52/120.69 tff(k1_lopclset_type, type, (
% 120.52/120.69 k1_lopclset: $i > $i)).
% 120.52/120.69 tff(m1_relset_1_type, type, (
% 120.52/120.69 m1_relset_1: ( $i * $i * $i ) > $o)).
% 120.52/120.69 tff(k2_zfmisc_1_type, type, (
% 120.52/120.69 k2_zfmisc_1: ( $i * $i ) > $i)).
% 120.52/120.69 tff(m2_relset_1_type, type, (
% 120.52/120.69 m2_relset_1: ( $i * $i * $i ) > $o)).
% 120.52/120.69 tff(v1_funct_2_type, type, (
% 120.52/120.69 v1_funct_2: ( $i * $i * $i ) > $o)).
% 120.52/120.69 tff(v1_funct_1_type, type, (
% 120.52/120.69 v1_funct_1: $i > $o)).
% 120.52/120.69 tff(m2_subset_1_type, type, (
% 120.52/120.69 m2_subset_1: ( $i * $i * $i ) > $o)).
% 120.52/120.69 tff(k1_zfmisc_1_type, type, (
% 120.52/120.69 k1_zfmisc_1: $i > $i)).
% 120.52/120.69 tff(v1_xboole_0_type, type, (
% 120.52/120.69 v1_xboole_0: $i > $o)).
% 120.52/120.69 tff(v4_finsub_1_type, type, (
% 120.52/120.69 v4_finsub_1: $i > $o)).
% 120.52/120.69 tff(v3_finsub_1_type, type, (
% 120.52/120.69 v3_finsub_1: $i > $o)).
% 120.52/120.69 tff(v1_finsub_1_type, type, (
% 120.52/120.69 v1_finsub_1: $i > $o)).
% 120.52/120.69 tff(1,plain,
% 120.52/120.69 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(2,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[1])).
% 120.52/120.69 tff(3,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite(((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))) <=> (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(4,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[3])).
% 120.52/120.69 tff(5,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(6,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), rewrite((((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A))) <=> ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(7,plain,
% 120.52/120.69 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[6])).
% 120.52/120.69 tff(8,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A))) & l3_lattices(k6_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_lopclset')).
% 120.52/120.69 tff(9,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[8, 7])).
% 120.52/120.69 tff(10,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[9, 5])).
% 120.52/120.69 tff(11,plain,(
% 120.52/120.69 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | ((~v3_struct_0(k6_lopclset(A))) & v10_lattices(k6_lopclset(A)) & l3_lattices(k6_lopclset(A))))),
% 120.52/120.69 inference(skolemize,[status(sab)],[10])).
% 120.52/120.69 tff(12,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[11, 4])).
% 120.52/120.69 tff(13,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[12, 2])).
% 120.52/120.69 tff(14,plain,
% 120.52/120.69 ((~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A)))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(15,plain,
% 120.52/120.69 ((~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A)))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(16,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_lopclset')).
% 120.52/120.69 tff(17,plain,
% 120.52/120.69 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[16, 15])).
% 120.52/120.69 tff(18,plain,
% 120.52/120.69 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[17, 14])).
% 120.52/120.69 tff(19,plain,
% 120.52/120.69 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[18, 14])).
% 120.52/120.69 tff(20,plain,
% 120.52/120.69 (~![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m1_subset_1(k2_pre_topc(A), u1_struct_0(k6_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[19, 14])).
% 120.52/120.69 tff(21,plain,(
% 120.52/120.69 ~((~((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0))) | m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))))),
% 120.52/120.69 inference(skolemize,[status(sab)],[20])).
% 120.52/120.69 tff(22,plain,
% 120.52/120.69 ((~v3_struct_0(A!0)) & v2_pre_topc(A!0) & l1_pre_topc(A!0)),
% 120.52/120.69 inference(or_elim,[status(thm)],[21])).
% 120.52/120.69 tff(23,plain,
% 120.52/120.69 (l1_pre_topc(A!0)),
% 120.52/120.69 inference(and_elim,[status(thm)],[22])).
% 120.52/120.69 tff(24,plain,
% 120.52/120.69 (v2_pre_topc(A!0)),
% 120.52/120.69 inference(and_elim,[status(thm)],[22])).
% 120.52/120.69 tff(25,plain,
% 120.52/120.69 (~v3_struct_0(A!0)),
% 120.52/120.69 inference(and_elim,[status(thm)],[22])).
% 120.52/120.69 tff(26,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(27,plain,
% 120.52/120.69 ((v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0)))))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(28,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0)))))))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[27])).
% 120.52/120.69 tff(29,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))))),
% 120.52/120.69 inference(transitivity,[status(thm)],[28, 26])).
% 120.52/120.69 tff(30,plain,
% 120.52/120.69 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~v10_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))))),
% 120.52/120.69 inference(quant_inst,[status(thm)],[])).
% 120.52/120.69 tff(31,plain,
% 120.52/120.69 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~(v3_struct_0(k6_lopclset(A)) | (~v10_lattices(k6_lopclset(A))) | (~l3_lattices(k6_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0)))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[30, 29])).
% 120.52/120.69 tff(32,plain,
% 120.52/120.69 (~(v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0))))),
% 120.52/120.69 inference(unit_resolution,[status(thm)],[31, 25, 24, 23, 13])).
% 120.52/120.69 tff(33,plain,
% 120.52/120.69 ((v3_struct_0(k6_lopclset(A!0)) | (~l3_lattices(k6_lopclset(A!0))) | (~v10_lattices(k6_lopclset(A!0)))) | l3_lattices(k6_lopclset(A!0))),
% 120.52/120.69 inference(tautology,[status(thm)],[])).
% 120.52/120.69 tff(34,plain,
% 120.52/120.69 (l3_lattices(k6_lopclset(A!0))),
% 120.52/120.69 inference(unit_resolution,[status(thm)],[33, 32])).
% 120.52/120.69 tff(35,plain,
% 120.52/120.69 (^[A: $i] : refl((v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(36,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[35])).
% 120.52/120.69 tff(37,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(38,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[37])).
% 120.52/120.69 tff(39,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(40,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(41,plain,
% 120.52/120.69 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[40])).
% 120.52/120.69 tff(42,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_lopclset')).
% 120.52/120.69 tff(43,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[42, 41])).
% 120.52/120.69 tff(44,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[43, 39])).
% 120.52/120.69 tff(45,plain,(
% 120.52/120.69 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))))),
% 120.52/120.69 inference(skolemize,[status(sab)],[44])).
% 120.52/120.69 tff(46,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[45, 38])).
% 120.52/120.69 tff(47,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[46, 36])).
% 120.52/120.69 tff(48,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(49,plain,
% 120.52/120.69 ((v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(50,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[49])).
% 120.52/120.69 tff(51,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))),
% 120.52/120.69 inference(transitivity,[status(thm)],[50, 48])).
% 120.52/120.69 tff(52,plain,
% 120.52/120.69 ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 120.52/120.69 inference(quant_inst,[status(thm)],[])).
% 120.52/120.69 tff(53,plain,
% 120.52/120.69 ((~![A: $i] : (v3_struct_0(A) | (k6_lopclset(A) = g3_lattices(k1_lopclset(A), k4_lopclset(A), k5_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[52, 51])).
% 120.52/120.69 tff(54,plain,
% 120.52/120.69 (k6_lopclset(A!0) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))),
% 120.52/120.69 inference(unit_resolution,[status(thm)],[53, 25, 24, 23, 47])).
% 120.52/120.69 tff(55,plain,
% 120.52/120.69 (g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = k6_lopclset(A!0)),
% 120.52/120.69 inference(symmetry,[status(thm)],[54])).
% 120.52/120.69 tff(56,plain,
% 120.52/120.69 (^[A: $i] : refl((v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A))) <=> (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(57,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[56])).
% 120.52/120.69 tff(58,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(59,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[58])).
% 120.52/120.69 tff(60,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(61,plain,
% 120.52/120.69 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(62,plain,
% 120.52/120.69 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => (k1_lopclset(A) = a_1_0_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[61])).
% 120.52/120.69 tff(63,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => (k1_lopclset(A) = a_1_0_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_lopclset')).
% 120.52/120.69 tff(64,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[63, 62])).
% 120.52/120.69 tff(65,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[64, 60])).
% 120.52/120.69 tff(66,plain,(
% 120.52/120.69 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | (k1_lopclset(A) = a_1_0_lopclset(A)))),
% 120.52/120.69 inference(skolemize,[status(sab)],[65])).
% 120.52/120.69 tff(67,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[66, 59])).
% 120.52/120.69 tff(68,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[67, 57])).
% 120.52/120.69 tff(69,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(70,plain,
% 120.52/120.69 ((v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(71,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0))))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[70])).
% 120.52/120.69 tff(72,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)))),
% 120.52/120.69 inference(transitivity,[status(thm)],[71, 69])).
% 120.52/120.69 tff(73,plain,
% 120.52/120.69 ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0)) | (~l1_pre_topc(A!0)))),
% 120.52/120.69 inference(quant_inst,[status(thm)],[])).
% 120.52/120.69 tff(74,plain,
% 120.52/120.69 ((~![A: $i] : (v3_struct_0(A) | (k1_lopclset(A) = a_1_0_lopclset(A)) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (k1_lopclset(A!0) = a_1_0_lopclset(A!0))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[73, 72])).
% 120.52/120.69 tff(75,plain,
% 120.52/120.69 (k1_lopclset(A!0) = a_1_0_lopclset(A!0)),
% 120.52/120.69 inference(unit_resolution,[status(thm)],[74, 25, 23, 68])).
% 120.52/120.69 tff(76,plain,
% 120.52/120.69 (a_1_0_lopclset(A!0) = k1_lopclset(A!0)),
% 120.52/120.69 inference(symmetry,[status(thm)],[75])).
% 120.52/120.69 tff(77,plain,
% 120.52/120.69 (g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(k1_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[76])).
% 120.52/120.69 tff(78,plain,
% 120.52/120.69 (g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = k6_lopclset(A!0)),
% 120.52/120.69 inference(transitivity,[status(thm)],[77, 55])).
% 120.52/120.69 tff(79,plain,
% 120.52/120.69 (v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))) <=> v3_lattices(k6_lopclset(A!0))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[78])).
% 120.52/120.69 tff(80,plain,
% 120.52/120.69 (k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)) = k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[76, 76])).
% 120.52/120.69 tff(81,plain,
% 120.52/120.69 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[80])).
% 120.52/120.69 tff(82,plain,
% 120.52/120.69 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.69 inference(symmetry,[status(thm)],[81])).
% 120.52/120.69 tff(83,plain,
% 120.52/120.69 (^[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)))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(84,plain,
% 120.52/120.69 (![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))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[83])).
% 120.52/120.69 tff(85,plain,
% 120.52/120.69 (![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))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(86,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 120.52/120.69 tff(87,plain,
% 120.52/120.69 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[86, 85])).
% 120.52/120.69 tff(88,plain,(
% 120.52/120.69 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 120.52/120.69 inference(skolemize,[status(sab)],[87])).
% 120.52/120.69 tff(89,plain,
% 120.52/120.69 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[88, 84])).
% 120.52/120.69 tff(90,plain,
% 120.52/120.69 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))),
% 120.52/120.69 inference(quant_inst,[status(thm)],[])).
% 120.52/120.69 tff(91,plain,
% 120.52/120.69 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.69 inference(unit_resolution,[status(thm)],[90, 89])).
% 120.52/120.69 tff(92,plain,
% 120.52/120.69 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.69 inference(monotonicity,[status(thm)],[76])).
% 120.52/120.69 tff(93,plain,
% 120.52/120.69 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.69 inference(symmetry,[status(thm)],[92])).
% 120.52/120.69 tff(94,plain,
% 120.52/120.69 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(95,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[94])).
% 120.52/120.69 tff(96,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(97,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[96])).
% 120.52/120.69 tff(98,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.69 inference(rewrite,[status(thm)],[])).
% 120.52/120.69 tff(99,plain,
% 120.52/120.69 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), rewrite(((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.69 inference(bind,[status(th)],[])).
% 120.52/120.69 tff(100,plain,
% 120.52/120.69 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.69 inference(quant_intro,[status(thm)],[99])).
% 120.52/120.69 tff(101,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lopclset')).
% 120.52/120.69 tff(102,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[101, 100])).
% 120.52/120.69 tff(103,plain,
% 120.52/120.69 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[102, 98])).
% 120.52/120.69 tff(104,plain,(
% 120.52/120.69 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k5_lopclset(A)) & v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.69 inference(skolemize,[status(sab)],[103])).
% 120.52/120.69 tff(105,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[104, 97])).
% 120.52/120.69 tff(106,plain,
% 120.52/120.69 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.69 inference(modus_ponens,[status(thm)],[105, 95])).
% 120.52/120.69 tff(107,plain,
% 120.52/120.69 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 120.52/120.70 inference(rewrite,[status(thm)],[])).
% 120.52/120.70 tff(108,plain,
% 120.52/120.70 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 120.52/120.70 inference(quant_inst,[status(thm)],[])).
% 120.52/120.70 tff(109,plain,
% 120.52/120.70 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k5_lopclset(A))) | (~v1_funct_2(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k5_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[108, 107])).
% 120.52/120.70 tff(110,plain,
% 120.52/120.70 (~((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[109, 25, 24, 23, 106])).
% 120.52/120.70 tff(111,plain,
% 120.52/120.70 (((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(112,plain,
% 120.52/120.70 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[111, 110])).
% 120.52/120.70 tff(113,plain,
% 120.52/120.70 (m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[112, 93])).
% 120.52/120.70 tff(114,plain,
% 120.52/120.70 ((~(m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))) | m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(115,plain,
% 120.52/120.70 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[114, 113, 91])).
% 120.52/120.70 tff(116,plain,
% 120.52/120.70 (m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[115, 82])).
% 120.52/120.70 tff(117,plain,
% 120.52/120.70 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(monotonicity,[status(thm)],[80, 76])).
% 120.52/120.70 tff(118,plain,
% 120.52/120.70 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(symmetry,[status(thm)],[117])).
% 120.52/120.70 tff(119,plain,
% 120.52/120.70 (^[A: $i] : refl((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))),
% 120.52/120.70 inference(bind,[status(th)],[])).
% 120.52/120.70 tff(120,plain,
% 120.52/120.70 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.70 inference(quant_intro,[status(thm)],[119])).
% 120.52/120.70 tff(121,plain,
% 120.52/120.70 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), rewrite((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))))),
% 120.52/120.70 inference(bind,[status(th)],[])).
% 120.52/120.70 tff(122,plain,
% 120.52/120.70 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.70 inference(quant_intro,[status(thm)],[121])).
% 120.52/120.70 tff(123,plain,
% 120.52/120.70 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.70 inference(rewrite,[status(thm)],[])).
% 120.52/120.70 tff(124,plain,
% 120.52/120.70 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), rewrite(((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) <=> (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.70 inference(bind,[status(th)],[])).
% 120.52/120.70 tff(125,plain,
% 120.52/120.70 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.70 inference(quant_intro,[status(thm)],[124])).
% 120.52/120.70 tff(126,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => ((v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lopclset')).
% 120.52/120.70 tff(127,plain,
% 120.52/120.70 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[126, 125])).
% 120.52/120.70 tff(128,plain,
% 120.52/120.70 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[127, 123])).
% 120.52/120.70 tff(129,plain,(
% 120.52/120.70 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | (v1_funct_1(k4_lopclset(A)) & v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A)) & m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))),
% 120.52/120.70 inference(skolemize,[status(sab)],[128])).
% 120.52/120.70 tff(130,plain,
% 120.52/120.70 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[129, 122])).
% 120.52/120.70 tff(131,plain,
% 120.52/120.70 (![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[130, 120])).
% 120.52/120.70 tff(132,plain,
% 120.52/120.70 (((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 120.52/120.70 inference(rewrite,[status(thm)],[])).
% 120.52/120.70 tff(133,plain,
% 120.52/120.70 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))))),
% 120.52/120.70 inference(quant_inst,[status(thm)],[])).
% 120.52/120.70 tff(134,plain,
% 120.52/120.70 ((~![A: $i] : (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)) | (~((~v1_funct_1(k4_lopclset(A))) | (~v1_funct_2(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))) | (~m2_relset_1(k4_lopclset(A), k2_zfmisc_1(k1_lopclset(A), k1_lopclset(A)), k1_lopclset(A))))))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[133, 132])).
% 120.52/120.70 tff(135,plain,
% 120.52/120.70 (~((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[134, 25, 24, 23, 131])).
% 120.52/120.70 tff(136,plain,
% 120.52/120.70 (((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(137,plain,
% 120.52/120.70 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[136, 135])).
% 120.52/120.70 tff(138,plain,
% 120.52/120.70 (v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[137, 118])).
% 120.52/120.70 tff(139,plain,
% 120.52/120.70 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(monotonicity,[status(thm)],[80, 76])).
% 120.52/120.70 tff(140,plain,
% 120.52/120.70 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(symmetry,[status(thm)],[139])).
% 120.52/120.70 tff(141,plain,
% 120.52/120.70 (((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(142,plain,
% 120.52/120.70 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[141, 110])).
% 120.52/120.70 tff(143,plain,
% 120.52/120.70 (v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[142, 140])).
% 120.52/120.70 tff(144,plain,
% 120.52/120.70 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(monotonicity,[status(thm)],[80])).
% 120.52/120.70 tff(145,plain,
% 120.52/120.70 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(symmetry,[status(thm)],[144])).
% 120.52/120.70 tff(146,plain,
% 120.52/120.70 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))),
% 120.52/120.70 inference(quant_inst,[status(thm)],[])).
% 120.52/120.70 tff(147,plain,
% 120.52/120.70 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[146, 89])).
% 120.52/120.70 tff(148,plain,
% 120.52/120.70 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(monotonicity,[status(thm)],[76])).
% 120.52/120.70 tff(149,plain,
% 120.52/120.70 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)) <=> m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(symmetry,[status(thm)],[148])).
% 120.52/120.70 tff(150,plain,
% 120.52/120.70 (((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(151,plain,
% 120.52/120.70 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[150, 135])).
% 120.52/120.70 tff(152,plain,
% 120.52/120.70 (m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[151, 149])).
% 120.52/120.70 tff(153,plain,
% 120.52/120.70 ((~(m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)) <=> m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0)))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))) | m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(154,plain,
% 120.52/120.70 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[153, 152, 147])).
% 120.52/120.70 tff(155,plain,
% 120.52/120.70 (m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[154, 145])).
% 120.52/120.70 tff(156,plain,
% 120.52/120.70 (((~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k4_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_1(k4_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(157,plain,
% 120.52/120.70 (v1_funct_1(k4_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[156, 135])).
% 120.52/120.70 tff(158,plain,
% 120.52/120.70 (((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0))) | (~m2_relset_1(k5_lopclset(A!0), k2_zfmisc_1(k1_lopclset(A!0), k1_lopclset(A!0)), k1_lopclset(A!0)))) | v1_funct_1(k5_lopclset(A!0))),
% 120.52/120.70 inference(tautology,[status(thm)],[])).
% 120.52/120.70 tff(159,plain,
% 120.52/120.70 (v1_funct_1(k5_lopclset(A!0))),
% 120.52/120.70 inference(unit_resolution,[status(thm)],[158, 110])).
% 120.52/120.70 tff(160,plain,
% 120.52/120.70 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 120.52/120.70 inference(bind,[status(th)],[])).
% 120.52/120.70 tff(161,plain,
% 120.52/120.70 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 120.52/120.70 inference(quant_intro,[status(thm)],[160])).
% 120.52/120.70 tff(162,plain,
% 120.52/120.70 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 120.52/120.70 inference(bind,[status(th)],[])).
% 120.52/120.70 tff(163,plain,
% 120.52/120.70 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 120.52/120.70 inference(quant_intro,[status(thm)],[162])).
% 120.52/120.70 tff(164,plain,
% 120.52/120.70 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 120.52/120.70 inference(rewrite,[status(thm)],[])).
% 120.52/120.70 tff(165,plain,
% 120.52/120.70 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 120.52/120.70 inference(bind,[status(th)],[])).
% 120.52/120.70 tff(166,plain,
% 120.52/120.70 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 120.52/120.70 inference(quant_intro,[status(thm)],[165])).
% 120.52/120.70 tff(167,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_g3_lattices')).
% 120.52/120.70 tff(168,plain,
% 120.52/120.70 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[167, 166])).
% 120.52/120.70 tff(169,plain,
% 120.52/120.70 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 120.52/120.70 inference(modus_ponens,[status(thm)],[168, 164])).
% 120.52/120.70 tff(170,plain,(
% 120.52/120.70 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 120.55/120.70 inference(skolemize,[status(sab)],[169])).
% 120.55/120.70 tff(171,plain,
% 120.55/120.70 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[170, 163])).
% 120.55/120.70 tff(172,plain,
% 120.55/120.70 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[171, 161])).
% 120.55/120.70 tff(173,plain,
% 120.55/120.70 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))))),
% 120.55/120.70 inference(rewrite,[status(thm)],[])).
% 120.55/120.70 tff(174,plain,
% 120.55/120.70 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))))),
% 120.55/120.70 inference(quant_inst,[status(thm)],[])).
% 120.55/120.70 tff(175,plain,
% 120.55/120.70 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[174, 173])).
% 120.55/120.70 tff(176,plain,
% 120.55/120.70 ((~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))))),
% 120.55/120.70 inference(unit_resolution,[status(thm)],[175, 172, 159, 157])).
% 120.55/120.70 tff(177,plain,
% 120.55/120.70 (~((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))))),
% 120.55/120.70 inference(unit_resolution,[status(thm)],[176, 155, 143, 138, 116])).
% 120.55/120.70 tff(178,plain,
% 120.55/120.70 (((~v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))) | (~l3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0))))) | v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))),
% 120.55/120.70 inference(tautology,[status(thm)],[])).
% 120.55/120.70 tff(179,plain,
% 120.55/120.70 (v3_lattices(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)))),
% 120.55/120.70 inference(unit_resolution,[status(thm)],[178, 177])).
% 120.55/120.70 tff(180,plain,
% 120.55/120.70 (v3_lattices(k6_lopclset(A!0))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[179, 79])).
% 120.55/120.70 tff(181,plain,
% 120.55/120.70 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 120.55/120.70 inference(bind,[status(th)],[])).
% 120.55/120.70 tff(182,plain,
% 120.55/120.70 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(quant_intro,[status(thm)],[181])).
% 120.55/120.70 tff(183,plain,
% 120.55/120.70 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(rewrite,[status(thm)],[])).
% 120.55/120.70 tff(184,plain,
% 120.55/120.70 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 120.55/120.70 inference(bind,[status(th)],[])).
% 120.55/120.70 tff(185,plain,
% 120.55/120.70 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(quant_intro,[status(thm)],[184])).
% 120.55/120.70 tff(186,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 120.55/120.70 tff(187,plain,
% 120.55/120.70 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[186, 185])).
% 120.55/120.70 tff(188,plain,
% 120.55/120.70 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[187, 183])).
% 120.55/120.70 tff(189,plain,(
% 120.55/120.70 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(skolemize,[status(sab)],[188])).
% 120.55/120.70 tff(190,plain,
% 120.55/120.70 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[189, 182])).
% 120.55/120.70 tff(191,plain,
% 120.55/120.70 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))),
% 120.55/120.70 inference(rewrite,[status(thm)],[])).
% 120.55/120.70 tff(192,plain,
% 120.55/120.70 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0))))),
% 120.55/120.70 inference(quant_inst,[status(thm)],[])).
% 120.55/120.70 tff(193,plain,
% 120.55/120.70 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0)))),
% 120.55/120.70 inference(modus_ponens,[status(thm)],[192, 191])).
% 120.55/120.70 tff(194,plain,
% 120.55/120.70 ((k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))) | (~v3_lattices(k6_lopclset(A!0))) | (~l3_lattices(k6_lopclset(A!0)))),
% 120.55/120.70 inference(unit_resolution,[status(thm)],[193, 190])).
% 120.55/120.70 tff(195,plain,
% 120.55/120.70 (k6_lopclset(A!0) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))),
% 120.55/120.70 inference(unit_resolution,[status(thm)],[194, 180, 34])).
% 120.55/120.70 tff(196,plain,
% 120.55/120.70 (g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0)))),
% 120.55/120.70 inference(transitivity,[status(thm)],[77, 55, 195])).
% 120.55/120.70 tff(197,plain,
% 120.55/120.70 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 120.55/120.70 inference(bind,[status(th)],[])).
% 120.55/120.70 tff(198,plain,
% 120.55/120.70 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 120.55/120.70 inference(quant_intro,[status(thm)],[197])).
% 120.55/120.70 tff(199,plain,
% 120.55/120.70 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 120.55/120.70 inference(bind,[status(th)],[])).
% 120.55/120.70 tff(200,plain,
% 120.55/120.70 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 120.55/120.70 inference(quant_intro,[status(thm)],[199])).
% 120.55/120.70 tff(201,plain,
% 120.55/120.70 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 120.55/120.70 inference(transitivity,[status(thm)],[200, 198])).
% 120.55/120.70 tff(202,plain,
% 120.55/120.70 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(203,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[202])).
% 120.55/120.71 tff(204,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(205,plain,
% 120.55/120.71 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(206,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[205])).
% 120.55/120.71 tff(207,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 120.55/120.71 tff(208,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[207, 206])).
% 120.55/120.71 tff(209,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[208, 204])).
% 120.55/120.71 tff(210,plain,(
% 120.55/120.71 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 120.55/120.71 inference(skolemize,[status(sab)],[209])).
% 120.55/120.71 tff(211,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[210, 203])).
% 120.55/120.71 tff(212,plain,
% 120.55/120.71 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[211, 201])).
% 120.55/120.71 tff(213,plain,
% 120.55/120.71 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F))))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(214,plain,
% 120.55/120.71 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F))))))),
% 120.55/120.71 inference(quant_inst,[status(thm)],[])).
% 120.55/120.71 tff(215,plain,
% 120.55/120.71 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(k5_lopclset(A!0))) | (~v1_funct_1(k4_lopclset(A!0))) | (~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[214, 213])).
% 120.55/120.71 tff(216,plain,
% 120.55/120.71 ((~v1_funct_2(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k4_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~v1_funct_2(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | (~m1_relset_1(k5_lopclset(A!0), k2_zfmisc_1(a_1_0_lopclset(A!0), a_1_0_lopclset(A!0)), a_1_0_lopclset(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[215, 212, 159, 157])).
% 120.55/120.71 tff(217,plain,
% 120.55/120.71 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[216, 155, 143, 138, 116])).
% 120.55/120.71 tff(218,plain,
% 120.55/120.71 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | (~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(219,plain,
% 120.55/120.71 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))))),
% 120.55/120.71 inference(quant_inst,[status(thm)],[])).
% 120.55/120.71 tff(220,plain,
% 120.55/120.71 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(D, E, F))) | (~((~(a_1_0_lopclset(A!0) = D)) | (~(k4_lopclset(A!0) = E)) | (~(k5_lopclset(A!0) = F)))))) | (~(g3_lattices(a_1_0_lopclset(A!0), k4_lopclset(A!0), k5_lopclset(A!0)) = g3_lattices(u1_struct_0(k6_lopclset(A!0)), u2_lattices(k6_lopclset(A!0)), u1_lattices(k6_lopclset(A!0))))) | (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0))))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[219, 218])).
% 120.55/120.71 tff(221,plain,
% 120.55/120.71 (~((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0)))))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[220, 217, 196])).
% 120.55/120.71 tff(222,plain,
% 120.55/120.71 (((~(a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))) | (~(k4_lopclset(A!0) = u2_lattices(k6_lopclset(A!0)))) | (~(k5_lopclset(A!0) = u1_lattices(k6_lopclset(A!0))))) | (a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0)))),
% 120.55/120.71 inference(tautology,[status(thm)],[])).
% 120.55/120.71 tff(223,plain,
% 120.55/120.71 (a_1_0_lopclset(A!0) = u1_struct_0(k6_lopclset(A!0))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[222, 221])).
% 120.55/120.71 tff(224,plain,
% 120.55/120.71 (r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) <=> r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[223])).
% 120.55/120.71 tff(225,plain,
% 120.55/120.71 (r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))) <=> r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 120.55/120.71 inference(symmetry,[status(thm)],[224])).
% 120.55/120.71 tff(226,plain,
% 120.55/120.71 ((~r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))) <=> (~r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[225])).
% 120.55/120.71 tff(227,plain,
% 120.55/120.71 (^[A: $i, B: $i] : refl(((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(228,plain,
% 120.55/120.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[227])).
% 120.55/120.71 tff(229,plain,
% 120.55/120.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(230,plain,
% 120.55/120.71 (^[A: $i, B: $i] : rewrite((r2_hidden(A, B) => m1_subset_1(A, B)) <=> ((~r2_hidden(A, B)) | m1_subset_1(A, B)))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(231,plain,
% 120.55/120.71 (![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B)) <=> ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[230])).
% 120.55/120.71 tff(232,axiom,(![A: $i, B: $i] : (r2_hidden(A, B) => m1_subset_1(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_subset')).
% 120.55/120.71 tff(233,plain,
% 120.55/120.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[232, 231])).
% 120.55/120.71 tff(234,plain,
% 120.55/120.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[233, 229])).
% 120.55/120.71 tff(235,plain,(
% 120.55/120.71 ![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(skolemize,[status(sab)],[234])).
% 120.55/120.71 tff(236,plain,
% 120.55/120.71 (![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[235, 228])).
% 120.55/120.71 tff(237,plain,
% 120.55/120.71 (~m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 120.55/120.71 inference(or_elim,[status(thm)],[21])).
% 120.55/120.71 tff(238,plain,
% 120.55/120.71 (((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))) | m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))) | m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(239,plain,
% 120.55/120.71 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | ((~r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))) | m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0))))),
% 120.55/120.71 inference(quant_inst,[status(thm)],[])).
% 120.55/120.71 tff(240,plain,
% 120.55/120.71 ((~![A: $i, B: $i] : ((~r2_hidden(A, B)) | m1_subset_1(A, B))) | (~r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))) | m1_subset_1(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[239, 238])).
% 120.55/120.71 tff(241,plain,
% 120.55/120.71 (~r2_hidden(k2_pre_topc(A!0), u1_struct_0(k6_lopclset(A!0)))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[240, 237, 236])).
% 120.55/120.71 tff(242,plain,
% 120.55/120.71 (~r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[241, 226])).
% 120.55/120.71 tff(243,plain,
% 120.55/120.71 (v1_xboole_0(a_1_0_lopclset(A!0)) <=> v1_xboole_0(k1_lopclset(A!0))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[76])).
% 120.55/120.71 tff(244,plain,
% 120.55/120.71 (v1_xboole_0(k1_lopclset(A!0)) <=> v1_xboole_0(a_1_0_lopclset(A!0))),
% 120.55/120.71 inference(symmetry,[status(thm)],[243])).
% 120.55/120.71 tff(245,plain,
% 120.55/120.71 ((~v1_xboole_0(k1_lopclset(A!0))) <=> (~v1_xboole_0(a_1_0_lopclset(A!0)))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[244])).
% 120.55/120.71 tff(246,plain,
% 120.55/120.71 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(247,plain,
% 120.55/120.71 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[246])).
% 120.55/120.71 tff(248,plain,
% 120.55/120.71 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> ((~v1_xboole_0(k1_lopclset(A))) | (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))), rewrite(((~v1_xboole_0(k1_lopclset(A))) | (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(249,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[248])).
% 120.55/120.71 tff(250,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)))) <=> ![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(251,plain,
% 120.55/120.71 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(252,plain,
% 120.55/120.71 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A)))) <=> ![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[251])).
% 120.55/120.71 tff(253,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => (~v1_xboole_0(k1_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_lopclset')).
% 120.55/120.71 tff(254,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[253, 252])).
% 120.55/120.71 tff(255,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[254, 250])).
% 120.55/120.71 tff(256,plain,(
% 120.55/120.71 ![A: $i] : ((~v1_xboole_0(k1_lopclset(A))) | (~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))))),
% 120.55/120.71 inference(skolemize,[status(sab)],[255])).
% 120.55/120.71 tff(257,plain,
% 120.55/120.71 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[256, 249])).
% 120.55/120.71 tff(258,plain,
% 120.55/120.71 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[257, 247])).
% 120.55/120.71 tff(259,plain,
% 120.55/120.71 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(260,plain,
% 120.55/120.71 ((v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(261,plain,
% 120.55/120.71 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0)))))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[260])).
% 120.55/120.71 tff(262,plain,
% 120.55/120.71 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0))))),
% 120.55/120.71 inference(transitivity,[status(thm)],[261, 259])).
% 120.55/120.71 tff(263,plain,
% 120.55/120.71 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(k1_lopclset(A!0))) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 120.55/120.71 inference(quant_inst,[status(thm)],[])).
% 120.55/120.71 tff(264,plain,
% 120.55/120.71 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(k1_lopclset(A))) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)) | (~v1_xboole_0(k1_lopclset(A!0)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[263, 262])).
% 120.55/120.71 tff(265,plain,
% 120.55/120.71 (~v1_xboole_0(k1_lopclset(A!0))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[264, 25, 24, 23, 258])).
% 120.55/120.71 tff(266,plain,
% 120.55/120.71 (~v1_xboole_0(a_1_0_lopclset(A!0))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[265, 245])).
% 120.55/120.71 tff(267,plain,
% 120.55/120.71 (^[A: $i] : refl((~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))) <=> (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(268,plain,
% 120.55/120.71 (![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))) <=> ![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[267])).
% 120.55/120.71 tff(269,plain,
% 120.55/120.71 (^[A: $i] : rewrite(((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A))) <=> (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A))))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(270,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A))) <=> ![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[269])).
% 120.55/120.71 tff(271,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A))) <=> ![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(272,plain,
% 120.55/120.71 (^[A: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) <=> ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)))), (((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> (((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))))), rewrite((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))), (((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(273,plain,
% 120.55/120.71 (![A: $i] : ((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A))) <=> ![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[272])).
% 120.55/120.71 tff(274,axiom,(![A: $i] : ((((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A))) & v3_finsub_1(k1_zfmisc_1(A))) & v4_finsub_1(k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_finsub_1')).
% 120.55/120.71 tff(275,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[274, 273])).
% 120.55/120.71 tff(276,plain,
% 120.55/120.71 (![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[275, 271])).
% 120.55/120.71 tff(277,plain,(
% 120.55/120.71 ![A: $i] : ((~v1_xboole_0(k1_zfmisc_1(A))) & v1_finsub_1(k1_zfmisc_1(A)) & v3_finsub_1(k1_zfmisc_1(A)) & v4_finsub_1(k1_zfmisc_1(A)))),
% 120.55/120.71 inference(skolemize,[status(sab)],[276])).
% 120.55/120.71 tff(278,plain,
% 120.55/120.71 (![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[277, 270])).
% 120.55/120.71 tff(279,plain,
% 120.55/120.71 (![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[278, 268])).
% 120.55/120.71 tff(280,plain,
% 120.55/120.71 ((~![A: $i] : (~(v1_xboole_0(k1_zfmisc_1(A)) | (~v1_finsub_1(k1_zfmisc_1(A))) | (~v3_finsub_1(k1_zfmisc_1(A))) | (~v4_finsub_1(k1_zfmisc_1(A)))))) | (~(v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | (~v1_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_finsub_1(k1_zfmisc_1(u1_struct_0(A!0))))))),
% 120.55/120.71 inference(quant_inst,[status(thm)],[])).
% 120.55/120.71 tff(281,plain,
% 120.55/120.71 (~(v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | (~v1_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[280, 279])).
% 120.55/120.71 tff(282,plain,
% 120.55/120.71 ((v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | (~v1_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v3_finsub_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~v4_finsub_1(k1_zfmisc_1(u1_struct_0(A!0))))) | (~v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))))),
% 120.55/120.71 inference(tautology,[status(thm)],[])).
% 120.55/120.71 tff(283,plain,
% 120.55/120.71 (~v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0)))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[282, 281])).
% 120.55/120.71 tff(284,plain,
% 120.55/120.71 (m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) <=> m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[76])).
% 120.55/120.71 tff(285,plain,
% 120.55/120.71 (m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) <=> m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 120.55/120.71 inference(symmetry,[status(thm)],[284])).
% 120.55/120.71 tff(286,plain,
% 120.55/120.71 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(287,plain,
% 120.55/120.71 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[286])).
% 120.55/120.71 tff(288,plain,
% 120.55/120.71 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A))))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)))), ((~((~v3_struct_0(A)) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A))))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))), (((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(289,plain,
% 120.55/120.71 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[288])).
% 120.55/120.71 tff(290,plain,
% 120.55/120.71 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(291,plain,
% 120.55/120.71 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_pre_topc(A)) => m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(292,plain,
% 120.55/120.71 (![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[291])).
% 120.55/120.71 tff(293,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_pre_topc(A)) => m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lopclset')).
% 120.55/120.71 tff(294,plain,
% 120.55/120.71 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[293, 292])).
% 120.55/120.71 tff(295,plain,
% 120.55/120.71 (![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[294, 290])).
% 120.55/120.71 tff(296,plain,(
% 120.55/120.71 ![A: $i] : ((~((~v3_struct_0(A)) & l1_pre_topc(A))) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))),
% 120.55/120.71 inference(skolemize,[status(sab)],[295])).
% 120.55/120.71 tff(297,plain,
% 120.55/120.71 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[296, 289])).
% 120.55/120.71 tff(298,plain,
% 120.55/120.71 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[297, 287])).
% 120.55/120.71 tff(299,plain,
% 120.55/120.71 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(300,plain,
% 120.55/120.71 ((v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0))) <=> (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 120.55/120.71 inference(rewrite,[status(thm)],[])).
% 120.55/120.71 tff(301,plain,
% 120.55/120.71 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))))),
% 120.55/120.71 inference(monotonicity,[status(thm)],[300])).
% 120.55/120.71 tff(302,plain,
% 120.55/120.71 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))))),
% 120.55/120.71 inference(transitivity,[status(thm)],[301, 299])).
% 120.55/120.71 tff(303,plain,
% 120.55/120.71 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | (v3_struct_0(A!0) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0)))) | (~l1_pre_topc(A!0)))),
% 120.55/120.71 inference(quant_inst,[status(thm)],[])).
% 120.55/120.71 tff(304,plain,
% 120.55/120.71 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k1_lopclset(A), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) | (~l1_pre_topc(A)))) | v3_struct_0(A!0) | (~l1_pre_topc(A!0)) | m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[303, 302])).
% 120.55/120.71 tff(305,plain,
% 120.55/120.71 (m1_subset_1(k1_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 120.55/120.71 inference(unit_resolution,[status(thm)],[304, 25, 23, 298])).
% 120.55/120.71 tff(306,plain,
% 120.55/120.71 (m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))),
% 120.55/120.71 inference(modus_ponens,[status(thm)],[305, 285])).
% 120.55/120.71 tff(307,plain,
% 120.55/120.71 (^[A: $i, B: $i] : rewrite((v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(308,plain,
% 120.55/120.71 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[307])).
% 120.55/120.71 tff(309,plain,
% 120.55/120.71 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(310,plain,
% 120.55/120.71 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 120.55/120.71 inference(quant_intro,[status(thm)],[309])).
% 120.55/120.71 tff(311,plain,
% 120.55/120.71 (^[A: $i, B: $i] : rewrite((v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 120.55/120.71 inference(bind,[status(th)],[])).
% 120.55/120.71 tff(312,plain,
% 120.55/120.71 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[311])).
% 120.55/120.72 tff(313,plain,
% 120.55/120.72 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 120.55/120.72 inference(transitivity,[status(thm)],[312, 310])).
% 120.55/120.72 tff(314,plain,
% 120.55/120.72 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ((v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))))), rewrite(((v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 120.55/120.72 inference(bind,[status(th)],[])).
% 120.55/120.72 tff(315,plain,
% 120.55/120.72 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[314])).
% 120.55/120.72 tff(316,plain,
% 120.55/120.72 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.72 inference(rewrite,[status(thm)],[])).
% 120.55/120.72 tff(317,plain,
% 120.55/120.72 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))))),
% 120.55/120.72 inference(bind,[status(th)],[])).
% 120.55/120.72 tff(318,plain,
% 120.55/120.72 (![A: $i, B: $i] : ((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[317])).
% 120.55/120.72 tff(319,axiom,(![A: $i, B: $i] : ((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_subset_1')).
% 120.55/120.72 tff(320,plain,
% 120.55/120.72 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[319, 318])).
% 120.55/120.72 tff(321,plain,
% 120.55/120.72 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[320, 316])).
% 120.55/120.72 tff(322,plain,(
% 120.55/120.72 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.72 inference(skolemize,[status(sab)],[321])).
% 120.55/120.72 tff(323,plain,
% 120.55/120.72 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[322, 315])).
% 120.55/120.72 tff(324,plain,
% 120.55/120.72 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[323, 313])).
% 120.55/120.72 tff(325,plain,
% 120.55/120.72 (![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[324, 308])).
% 120.55/120.72 tff(326,plain,
% 120.55/120.72 (((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 120.55/120.72 inference(rewrite,[status(thm)],[])).
% 120.55/120.72 tff(327,plain,
% 120.55/120.72 ((v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))) <=> (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 120.55/120.72 inference(rewrite,[status(thm)],[])).
% 120.55/120.72 tff(328,plain,
% 120.55/120.72 (((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))))),
% 120.55/120.72 inference(monotonicity,[status(thm)],[327])).
% 120.55/120.72 tff(329,plain,
% 120.55/120.72 (((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 120.55/120.72 inference(transitivity,[status(thm)],[328, 326])).
% 120.55/120.72 tff(330,plain,
% 120.55/120.72 ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | (v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0))))),
% 120.55/120.72 inference(quant_inst,[status(thm)],[])).
% 120.55/120.72 tff(331,plain,
% 120.55/120.72 ((~![A: $i, B: $i] : (v1_xboole_0(A) | v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : (m2_subset_1(C, A, B) <=> m1_subset_1(C, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[330, 329])).
% 120.55/120.72 tff(332,plain,
% 120.55/120.72 (v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(a_1_0_lopclset(A!0), k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A!0))))) | v1_xboole_0(k1_zfmisc_1(u1_struct_0(A!0))) | ![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))),
% 120.55/120.72 inference(unit_resolution,[status(thm)],[331, 325])).
% 120.55/120.72 tff(333,plain,
% 120.55/120.72 (![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))),
% 120.55/120.72 inference(unit_resolution,[status(thm)],[332, 306, 283, 266])).
% 120.55/120.72 tff(334,plain,
% 120.55/120.72 ((~![C: $i] : (m2_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(C, a_1_0_lopclset(A!0)))) | (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))),
% 120.55/120.72 inference(quant_inst,[status(thm)],[])).
% 120.55/120.72 tff(335,plain,
% 120.55/120.72 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 120.55/120.72 inference(unit_resolution,[status(thm)],[334, 333])).
% 120.55/120.72 tff(336,plain,
% 120.55/120.72 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0))),
% 120.55/120.72 inference(monotonicity,[status(thm)],[76])).
% 120.55/120.72 tff(337,plain,
% 120.55/120.72 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) <=> m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0))),
% 120.55/120.72 inference(symmetry,[status(thm)],[336])).
% 120.55/120.72 tff(338,plain,
% 120.55/120.72 (^[A: $i] : refl((v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))),
% 120.55/120.72 inference(bind,[status(th)],[])).
% 120.55/120.72 tff(339,plain,
% 120.55/120.72 (![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) <=> ![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[338])).
% 120.55/120.72 tff(340,plain,
% 120.55/120.72 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) <=> (~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) <=> (v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))))), rewrite(((v3_struct_0(A) | (~l1_pre_topc(A)) | (~v2_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))), (((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))))),
% 120.55/120.72 inference(bind,[status(th)],[])).
% 120.55/120.72 tff(341,plain,
% 120.55/120.72 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[340])).
% 120.55/120.72 tff(342,plain,
% 120.55/120.72 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 120.55/120.72 inference(rewrite,[status(thm)],[])).
% 120.55/120.72 tff(343,plain,
% 120.55/120.72 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) <=> ((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> (((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))), (((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))))),
% 120.55/120.72 inference(bind,[status(th)],[])).
% 120.55/120.72 tff(344,plain,
% 120.55/120.72 (![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[343])).
% 120.55/120.72 tff(345,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v2_pre_topc(A)) & l1_pre_topc(A)) => m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_lopclset')).
% 120.55/120.72 tff(346,plain,
% 120.55/120.72 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[345, 344])).
% 120.55/120.72 tff(347,plain,
% 120.55/120.72 (![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[346, 342])).
% 120.55/120.72 tff(348,plain,(
% 120.55/120.72 ![A: $i] : ((~((~v3_struct_0(A)) & v2_pre_topc(A) & l1_pre_topc(A))) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)))),
% 120.55/120.72 inference(skolemize,[status(sab)],[347])).
% 120.55/120.72 tff(349,plain,
% 120.55/120.72 (![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[348, 341])).
% 120.55/120.72 tff(350,plain,
% 120.55/120.72 (![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[349, 339])).
% 120.55/120.72 tff(351,plain,
% 120.55/120.72 (((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 120.55/120.72 inference(rewrite,[status(thm)],[])).
% 120.55/120.72 tff(352,plain,
% 120.55/120.72 ((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | (v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0)))),
% 120.55/120.72 inference(quant_inst,[status(thm)],[])).
% 120.55/120.72 tff(353,plain,
% 120.55/120.72 ((~![A: $i] : (v3_struct_0(A) | m2_subset_1(k2_pre_topc(A), k1_zfmisc_1(u1_struct_0(A)), k1_lopclset(A)) | (~l1_pre_topc(A)) | (~v2_pre_topc(A)))) | v3_struct_0(A!0) | m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0)) | (~l1_pre_topc(A!0)) | (~v2_pre_topc(A!0))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[352, 351])).
% 120.55/120.72 tff(354,plain,
% 120.55/120.72 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), k1_lopclset(A!0))),
% 120.55/120.72 inference(unit_resolution,[status(thm)],[353, 25, 24, 23, 350])).
% 120.55/120.72 tff(355,plain,
% 120.55/120.72 (m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0))),
% 120.55/120.72 inference(modus_ponens,[status(thm)],[354, 337])).
% 120.55/120.72 tff(356,plain,
% 120.55/120.72 ((~(m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0)) <=> m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))) | (~m2_subset_1(k2_pre_topc(A!0), k1_zfmisc_1(u1_struct_0(A!0)), a_1_0_lopclset(A!0))) | m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 120.55/120.72 inference(tautology,[status(thm)],[])).
% 120.55/120.72 tff(357,plain,
% 120.55/120.72 (m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 120.55/120.72 inference(unit_resolution,[status(thm)],[356, 355, 335])).
% 120.55/120.72 tff(358,plain,
% 120.55/120.72 (^[A: $i, B: $i] : refl((r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 120.55/120.72 inference(bind,[status(th)],[])).
% 120.55/120.72 tff(359,plain,
% 120.55/120.72 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.55/120.72 inference(quant_intro,[status(thm)],[358])).
% 120.55/120.72 tff(360,plain,
% 120.55/120.72 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.55/120.72 inference(rewrite,[status(thm)],[])).
% 120.57/120.72 tff(361,plain,
% 120.57/120.72 (^[A: $i, B: $i] : rewrite((m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B))))),
% 120.57/120.72 inference(bind,[status(th)],[])).
% 120.57/120.72 tff(362,plain,
% 120.57/120.72 (![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B))) <=> ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.57/120.72 inference(quant_intro,[status(thm)],[361])).
% 120.57/120.72 tff(363,axiom,(![A: $i, B: $i] : (m1_subset_1(A, B) => (v1_xboole_0(B) | r2_hidden(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 120.57/120.72 tff(364,plain,
% 120.57/120.72 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.57/120.72 inference(modus_ponens,[status(thm)],[363, 362])).
% 120.57/120.72 tff(365,plain,
% 120.57/120.72 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.57/120.72 inference(modus_ponens,[status(thm)],[364, 360])).
% 120.57/120.72 tff(366,plain,(
% 120.57/120.72 ![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.57/120.72 inference(skolemize,[status(sab)],[365])).
% 120.57/120.72 tff(367,plain,
% 120.57/120.72 (![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))),
% 120.57/120.72 inference(modus_ponens,[status(thm)],[366, 359])).
% 120.57/120.72 tff(368,plain,
% 120.57/120.72 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(a_1_0_lopclset(A!0)) | r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))),
% 120.57/120.72 inference(rewrite,[status(thm)],[])).
% 120.57/120.72 tff(369,plain,
% 120.57/120.72 ((r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))) <=> (v1_xboole_0(a_1_0_lopclset(A!0)) | r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))),
% 120.57/120.72 inference(rewrite,[status(thm)],[])).
% 120.57/120.72 tff(370,plain,
% 120.57/120.72 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (v1_xboole_0(a_1_0_lopclset(A!0)) | r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))))),
% 120.57/120.72 inference(monotonicity,[status(thm)],[369])).
% 120.57/120.72 tff(371,plain,
% 120.57/120.72 (((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))) <=> ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))),
% 120.57/120.72 inference(transitivity,[status(thm)],[370, 368])).
% 120.57/120.72 tff(372,plain,
% 120.57/120.72 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | (r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | v1_xboole_0(a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0))))),
% 120.57/120.72 inference(quant_inst,[status(thm)],[])).
% 120.57/120.72 tff(373,plain,
% 120.57/120.72 ((~![A: $i, B: $i] : (r2_hidden(A, B) | v1_xboole_0(B) | (~m1_subset_1(A, B)))) | v1_xboole_0(a_1_0_lopclset(A!0)) | r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))),
% 120.57/120.72 inference(modus_ponens,[status(thm)],[372, 371])).
% 120.57/120.72 tff(374,plain,
% 120.57/120.72 (r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0)) | (~m1_subset_1(k2_pre_topc(A!0), a_1_0_lopclset(A!0)))),
% 120.57/120.72 inference(unit_resolution,[status(thm)],[373, 367, 266])).
% 120.57/120.72 tff(375,plain,
% 120.57/120.72 (r2_hidden(k2_pre_topc(A!0), a_1_0_lopclset(A!0))),
% 120.57/120.72 inference(unit_resolution,[status(thm)],[374, 357])).
% 120.57/120.72 tff(376,plain,
% 120.57/120.72 ($false),
% 121.19/121.35 inference(unit_resolution,[status(thm)],[375, 242])).
% 121.19/121.35 % SZS output end Proof
% 121.19/121.35 % E exiting
%------------------------------------------------------------------------------