%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT292+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:14:12 AM UTC 2025
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT292+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 20:03:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(r1_filter_1_type, type, (
% 0.19/0.45 r1_filter_1: ( $i * $i ) > $o)).
% 0.19/0.45 tff(k6_lopclset_type, type, (
% 0.19/0.45 k6_lopclset: $i > $i)).
% 0.19/0.45 tff(k11_lopclset_type, type, (
% 0.19/0.45 k11_lopclset: $i > $i)).
% 0.19/0.45 tff(tptp_fun_A_0_type, type, (
% 0.19/0.45 tptp_fun_A_0: $i)).
% 0.19/0.45 tff(k12_lopclset_type, type, (
% 0.19/0.45 k12_lopclset: $i > $i)).
% 0.19/0.45 tff(v17_lattices_type, type, (
% 0.19/0.45 v17_lattices: $i > $o)).
% 0.19/0.45 tff(v10_lattices_type, type, (
% 0.19/0.45 v10_lattices: $i > $o)).
% 0.19/0.45 tff(l3_lattices_type, type, (
% 0.19/0.45 l3_lattices: $i > $o)).
% 0.19/0.45 tff(v3_struct_0_type, type, (
% 0.19/0.45 v3_struct_0: $i > $o)).
% 0.19/0.45 tff(v3_realset2_type, type, (
% 0.19/0.45 v3_realset2: $i > $o)).
% 0.19/0.45 tff(l1_pre_topc_type, type, (
% 0.19/0.45 l1_pre_topc: $i > $o)).
% 0.19/0.45 tff(v2_pre_topc_type, type, (
% 0.19/0.45 v2_pre_topc: $i > $o)).
% 0.19/0.45 tff(v1_pre_topc_type, type, (
% 0.19/0.45 v1_pre_topc: $i > $o)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.45 tff(8,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_lopclset')).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.45 tff(11,plain,(
% 0.19/0.45 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[10])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.45 tff(13,plain,
% 0.19/0.45 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.46 tff(14,plain,
% 0.19/0.46 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0)) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(15,plain,
% 0.19/0.46 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(16,plain,
% 0.19/0.46 ((~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ?[B: $i] : ((((~v3_struct_0(B)) & v2_pre_topc(B)) & l1_pre_topc(B)) & r1_filter_1(A, k6_lopclset(B))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(17,axiom,(~![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ?[B: $i] : ((((~v3_struct_0(B)) & v2_pre_topc(B)) & l1_pre_topc(B)) & r1_filter_1(A, k6_lopclset(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t44_lopclset')).
% 0.19/0.46 tff(18,plain,
% 0.19/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.46 tff(19,plain,
% 0.19/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.19/0.46 tff(20,plain,
% 0.19/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.46 tff(21,plain,
% 0.19/0.46 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ?[B: $i] : ((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A, k6_lopclset(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[20, 15])).
% 0.19/0.46 tff(22,plain,
% 0.19/0.46 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & (~v3_realset2(A!0)) & l3_lattices(A!0) & ![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.46 tff(23,plain,
% 0.19/0.46 (l3_lattices(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[22])).
% 0.19/0.46 tff(24,plain,
% 0.19/0.46 (~v3_realset2(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[22])).
% 0.19/0.46 tff(25,plain,
% 0.19/0.46 (v17_lattices(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[22])).
% 0.19/0.46 tff(26,plain,
% 0.19/0.46 (v10_lattices(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[22])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (~v3_struct_0(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[22])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 ((v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))) <=> (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0)))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[30, 28])).
% 0.19/0.46 tff(32,plain,
% 0.19/0.46 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (k12_lopclset(A) = k6_lopclset(k11_lopclset(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (k12_lopclset(A!0) = k6_lopclset(k11_lopclset(A!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[33, 27, 26, 25, 24, 23, 13])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (k6_lopclset(k11_lopclset(A!0)) = k12_lopclset(A!0)),
% 0.19/0.46 inference(symmetry,[status(thm)],[34])).
% 0.19/0.46 tff(36,plain,
% 0.19/0.46 (r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0))) <=> r1_filter_1(A!0, k12_lopclset(A!0))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[35])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (r1_filter_1(A!0, k12_lopclset(A!0)) <=> r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))),
% 0.19/0.46 inference(symmetry,[status(thm)],[36])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | r1_filter_1(A, k12_lopclset(A))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.46 tff(45,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => r1_filter_1(A, k12_lopclset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_lopclset')).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.19/0.46 tff(48,plain,(
% 0.19/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | r1_filter_1(A, k12_lopclset(A)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[47])).
% 0.19/0.46 tff(49,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.19/0.46 tff(50,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.19/0.46 tff(51,plain,
% 0.19/0.46 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(52,plain,
% 0.19/0.46 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | (v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(53,plain,
% 0.19/0.46 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | r1_filter_1(A, k12_lopclset(A)) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))) | v3_realset2(A!0) | v3_struct_0(A!0) | r1_filter_1(A!0, k12_lopclset(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.46 tff(54,plain,
% 0.19/0.46 (r1_filter_1(A!0, k12_lopclset(A!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[53, 27, 26, 25, 24, 23, 50])).
% 0.19/0.46 tff(55,plain,
% 0.19/0.46 (r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[54, 37])).
% 0.19/0.46 tff(56,plain,
% 0.19/0.46 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(57,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.46 tff(58,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite(((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) <=> (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.46 tff(60,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A))) <=> ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.46 tff(63,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => (((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A))) & v2_pre_topc(k11_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_lopclset')).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.19/0.46 tff(66,plain,(
% 0.19/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | ((~v3_struct_0(k11_lopclset(A))) & v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[65])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k11_lopclset(A)) | (~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 (~(v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[71, 27, 26, 25, 24, 23, 68])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 ((v3_struct_0(k11_lopclset(A!0)) | (~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0)))) | (~v3_struct_0(k11_lopclset(A!0)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 (~v3_struct_0(k11_lopclset(A!0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (^[A: $i] : refl((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) <=> (~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))) <=> (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))))), rewrite(((v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A)))))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)))), rewrite(((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A))) <=> (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A)) => (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(81,plain,
% 0.19/0.47 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.47 tff(82,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & (~v3_realset2(A))) & l3_lattices(A)) => ((v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A))) & l1_pre_topc(k11_lopclset(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k11_lopclset')).
% 0.19/0.47 tff(83,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.19/0.47 tff(85,plain,(
% 0.19/0.47 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & (~v3_realset2(A)) & l3_lattices(A))) | (v1_pre_topc(k11_lopclset(A)) & v2_pre_topc(k11_lopclset(A)) & l1_pre_topc(k11_lopclset(A))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[84])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 (![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[86, 76])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))))) <=> ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | (v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 ((~![A: $i] : (v3_realset2(A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~((~v1_pre_topc(k11_lopclset(A))) | (~v2_pre_topc(k11_lopclset(A))) | (~l1_pre_topc(k11_lopclset(A))))))) | v3_realset2(A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (~((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[90, 27, 26, 25, 24, 23, 87])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0)))) | l1_pre_topc(k11_lopclset(A!0))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (l1_pre_topc(k11_lopclset(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (((~v1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~l1_pre_topc(k11_lopclset(A!0)))) | v2_pre_topc(k11_lopclset(A!0))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (v2_pre_topc(k11_lopclset(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[94, 91])).
% 0.19/0.47 tff(96,plain,
% 0.19/0.47 (^[B: $i] : refl((v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))) <=> (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (^[B: $i] : trans(monotonicity(rewrite(((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))) <=> (~(v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))), ((~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))) <=> (~(~(v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))))), rewrite((~(~(v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B)))))) <=> (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))), ((~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))) <=> (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(99,plain,
% 0.19/0.47 (![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (![B: $i] : (~((~v3_struct_0(B)) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A!0, k6_lopclset(B))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[22])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | (v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 ((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | (v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ((~![B: $i] : (v3_struct_0(B) | (~l1_pre_topc(B)) | (~v2_pre_topc(B)) | (~r1_filter_1(A!0, k6_lopclset(B))))) | v3_struct_0(k11_lopclset(A!0)) | (~l1_pre_topc(k11_lopclset(A!0))) | (~v2_pre_topc(k11_lopclset(A!0))) | (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (~r1_filter_1(A!0, k6_lopclset(k11_lopclset(A!0)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[105, 102, 95, 93, 74])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[106, 55])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------