%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT313+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:18 AM UTC 2025
% Result : Theorem 0.18s 0.43s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT313+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n010.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Thu Jun 19 20:12:41 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % SZS output start Proof
% 0.18/0.43 tff(r1_filter_2_type, type, (
% 0.18/0.43 r1_filter_2: ( $i * $i * $i ) > $o)).
% 0.18/0.43 tff(k17_filter_2_type, type, (
% 0.18/0.43 k17_filter_2: $i > $i)).
% 0.18/0.43 tff(tptp_fun_A_0_type, type, (
% 0.18/0.43 tptp_fun_A_0: $i)).
% 0.18/0.43 tff(tptp_fun_B_1_type, type, (
% 0.18/0.43 tptp_fun_B_1: $i)).
% 0.18/0.43 tff(u1_struct_0_type, type, (
% 0.18/0.43 u1_struct_0: $i > $i)).
% 0.18/0.43 tff(k19_filter_2_type, type, (
% 0.18/0.43 k19_filter_2: ( $i * $i ) > $i)).
% 0.18/0.43 tff(v10_lattices_type, type, (
% 0.18/0.43 v10_lattices: $i > $o)).
% 0.18/0.43 tff(l3_lattices_type, type, (
% 0.18/0.43 l3_lattices: $i > $o)).
% 0.18/0.43 tff(v3_struct_0_type, type, (
% 0.18/0.43 v3_struct_0: $i > $o)).
% 0.18/0.43 tff(m2_filter_2_type, type, (
% 0.18/0.43 m2_filter_2: ( $i * $i ) > $o)).
% 0.18/0.43 tff(r2_hidden_type, type, (
% 0.18/0.43 r2_hidden: ( $i * $i ) > $o)).
% 0.18/0.43 tff(k6_lattices_type, type, (
% 0.18/0.43 k6_lattices: $i > $i)).
% 0.18/0.43 tff(v14_lattices_type, type, (
% 0.18/0.43 v14_lattices: $i > $o)).
% 0.18/0.43 tff(m1_subset_1_type, type, (
% 0.18/0.43 m1_subset_1: ( $i * $i ) > $o)).
% 0.18/0.43 tff(k1_zfmisc_1_type, type, (
% 0.18/0.43 k1_zfmisc_1: $i > $i)).
% 0.18/0.43 tff(m2_lattice4_type, type, (
% 0.18/0.43 m2_lattice4: ( $i * $i ) > $o)).
% 0.18/0.43 tff(v1_xboole_0_type, type, (
% 0.18/0.43 v1_xboole_0: $i > $o)).
% 0.18/0.43 tff(l1_struct_0_type, type, (
% 0.18/0.43 l1_struct_0: $i > $o)).
% 0.18/0.43 tff(l2_lattices_type, type, (
% 0.18/0.43 l2_lattices: $i > $o)).
% 0.18/0.43 tff(l1_lattices_type, type, (
% 0.18/0.43 l1_lattices: $i > $o)).
% 0.18/0.43 tff(1,plain,
% 0.18/0.43 (^[A: $i] : refl((v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(2,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.43 tff(3,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(4,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.43 tff(5,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(6,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(7,plain,
% 0.18/0.43 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.43 tff(8,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_filter_2')).
% 0.18/0.43 tff(9,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.43 tff(10,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.43 tff(11,plain,(
% 0.18/0.43 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.18/0.43 inference(skolemize,[status(sab)],[10])).
% 0.18/0.43 tff(12,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.18/0.43 tff(13,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.18/0.43 tff(14,plain,
% 0.18/0.43 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(15,plain,
% 0.18/0.43 ((~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))) <=> (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(16,plain,
% 0.18/0.43 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.43 tff(17,plain,
% 0.18/0.43 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.43 tff(18,plain,
% 0.18/0.43 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(19,plain,
% 0.18/0.43 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(20,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t43_filter_2')).
% 0.18/0.43 tff(21,plain,
% 0.18/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.18/0.43 tff(22,plain,
% 0.18/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.18/0.43 tff(23,plain,
% 0.18/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.43 tff(24,plain,
% 0.18/0.43 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), B, k17_filter_2(A)) & (B = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~m2_filter_2(B, A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.18/0.43 tff(25,plain,
% 0.18/0.43 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.43 tff(26,plain,
% 0.18/0.43 (l3_lattices(A!0)),
% 0.18/0.43 inference(and_elim,[status(thm)],[25])).
% 0.18/0.43 tff(27,plain,
% 0.18/0.43 (v10_lattices(A!0)),
% 0.18/0.43 inference(and_elim,[status(thm)],[25])).
% 0.18/0.43 tff(28,plain,
% 0.18/0.43 (~v3_struct_0(A!0)),
% 0.18/0.43 inference(and_elim,[status(thm)],[25])).
% 0.18/0.43 tff(29,plain,
% 0.18/0.43 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(30,plain,
% 0.18/0.43 ((v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(31,plain,
% 0.18/0.43 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[30])).
% 0.18/0.43 tff(32,plain,
% 0.18/0.43 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.18/0.43 inference(transitivity,[status(thm)],[31, 29])).
% 0.18/0.43 tff(33,plain,
% 0.18/0.43 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(34,plain,
% 0.18/0.43 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.43 tff(35,plain,
% 0.18/0.43 (k17_filter_2(A!0) = u1_struct_0(A!0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[34, 28, 27, 26, 13])).
% 0.18/0.43 tff(36,plain,
% 0.18/0.43 (u1_struct_0(A!0) = k17_filter_2(A!0)),
% 0.18/0.43 inference(symmetry,[status(thm)],[35])).
% 0.18/0.43 tff(37,plain,
% 0.18/0.43 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(38,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.43 tff(39,plain,
% 0.18/0.43 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(40,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[39])).
% 0.18/0.43 tff(41,plain,
% 0.18/0.43 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[40, 38])).
% 0.18/0.43 tff(42,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(43,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[42])).
% 0.18/0.43 tff(44,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(45,plain,
% 0.18/0.43 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(46,plain,
% 0.18/0.43 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.43 tff(47,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.18/0.43 tff(48,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.43 tff(49,plain,
% 0.18/0.43 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.18/0.44 tff(50,plain,(
% 0.18/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[49])).
% 0.18/0.44 tff(51,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.18/0.44 tff(52,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.18/0.44 tff(53,plain,
% 0.18/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(54,plain,
% 0.18/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(55,plain,
% 0.18/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.44 tff(56,plain,
% 0.18/0.44 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[55, 28, 27, 26, 52])).
% 0.18/0.44 tff(57,plain,
% 0.18/0.44 (~((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) | (~(v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1))) | (~m2_filter_2(B!1, A!0)))),
% 0.18/0.44 inference(and_elim,[status(thm)],[25])).
% 0.18/0.44 tff(58,plain,
% 0.18/0.44 (m2_filter_2(B!1, A!0)),
% 0.18/0.44 inference(or_elim,[status(thm)],[57])).
% 0.18/0.44 tff(59,plain,
% 0.18/0.44 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(60,plain,
% 0.18/0.44 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(61,plain,
% 0.18/0.44 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.44 tff(62,plain,
% 0.18/0.44 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[61, 58, 56])).
% 0.18/0.44 tff(63,plain,
% 0.18/0.44 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(64,plain,
% 0.18/0.44 (m2_lattice4(B!1, A!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.18/0.44 tff(65,plain,
% 0.18/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(66,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.44 tff(67,plain,
% 0.18/0.44 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(68,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.44 tff(69,plain,
% 0.18/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(70,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.18/0.44 tff(71,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[70, 68])).
% 0.18/0.44 tff(72,plain,
% 0.18/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(73,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.18/0.44 tff(74,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(75,plain,
% 0.18/0.44 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(76,plain,
% 0.18/0.44 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.44 tff(77,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.18/0.44 tff(78,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.44 tff(79,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.18/0.44 tff(80,plain,(
% 0.18/0.44 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[79])).
% 0.18/0.44 tff(81,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.18/0.44 tff(82,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.18/0.44 tff(83,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[82, 66])).
% 0.18/0.44 tff(84,plain,
% 0.18/0.44 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(85,plain,
% 0.18/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(86,plain,
% 0.18/0.44 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.44 tff(87,plain,
% 0.18/0.44 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[86, 28, 27, 26, 83])).
% 0.18/0.44 tff(88,plain,
% 0.18/0.44 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(89,plain,
% 0.18/0.44 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(90,plain,
% 0.18/0.44 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.18/0.44 tff(91,plain,
% 0.18/0.44 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[90, 87, 64])).
% 0.18/0.44 tff(92,plain,
% 0.18/0.44 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(93,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[92])).
% 0.18/0.44 tff(94,plain,
% 0.18/0.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(95,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[94])).
% 0.18/0.44 tff(96,plain,
% 0.18/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[95, 93])).
% 0.18/0.44 tff(97,plain,
% 0.18/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) <=> (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A)))))), trans(monotonicity(rewrite((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) <=> (~((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) <=> (~(~((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))))), rewrite((~(~((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))) <=> ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))), ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) <=> ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))) | (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite(((~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | ((~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))) | (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))), (((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))), (![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(98,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[97])).
% 0.18/0.44 tff(99,plain,
% 0.18/0.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(100,plain,
% 0.18/0.44 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))) <=> ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(101,plain,
% 0.18/0.45 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[100])).
% 0.18/0.45 tff(102,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ((v14_lattices(A) & r2_hidden(k6_lattices(A), B)) => (r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t42_filter_2')).
% 0.18/0.45 tff(103,plain,
% 0.18/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.45 tff(104,plain,
% 0.18/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.18/0.45 tff(105,plain,(
% 0.18/0.45 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A)) & (k19_filter_2(A, B) = u1_struct_0(A))) | (~(v14_lattices(A) & r2_hidden(k6_lattices(A), B))) | (~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[104])).
% 0.18/0.45 tff(106,plain,
% 0.18/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.18/0.45 tff(107,plain,
% 0.18/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.18/0.45 tff(108,plain,
% 0.18/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(109,plain,
% 0.18/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(110,plain,
% 0.18/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), k17_filter_2(A))) | (~(k19_filter_2(A, B) = u1_struct_0(A))))) | (~v14_lattices(A)) | (~r2_hidden(k6_lattices(A), B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.18/0.45 tff(111,plain,
% 0.18/0.45 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[110, 28, 27, 26, 107])).
% 0.18/0.45 tff(112,plain,
% 0.18/0.45 (^[A: $i, B: $i] : refl(((~v1_xboole_0(B)) | (~r2_hidden(A, B))) <=> ((~v1_xboole_0(B)) | (~r2_hidden(A, B))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(113,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[112])).
% 0.18/0.45 tff(114,plain,
% 0.18/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite((r2_hidden(A, B) & v1_xboole_0(B)) <=> (~((~v1_xboole_0(B)) | (~r2_hidden(A, B))))), ((~(r2_hidden(A, B) & v1_xboole_0(B))) <=> (~(~((~v1_xboole_0(B)) | (~r2_hidden(A, B))))))), rewrite((~(~((~v1_xboole_0(B)) | (~r2_hidden(A, B))))) <=> ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))), ((~(r2_hidden(A, B) & v1_xboole_0(B))) <=> ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(115,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.18/0.45 tff(116,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B))) <=> ![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(117,axiom,(![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 0.18/0.45 tff(118,plain,
% 0.18/0.45 (![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.18/0.45 tff(119,plain,(
% 0.18/0.45 ![A: $i, B: $i] : (~(r2_hidden(A, B) & v1_xboole_0(B)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[118])).
% 0.18/0.45 tff(120,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.18/0.45 tff(121,plain,
% 0.18/0.45 (![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.18/0.45 tff(122,plain,
% 0.18/0.45 (v14_lattices(A!0) & r2_hidden(k6_lattices(A!0), B!1)),
% 0.18/0.45 inference(or_elim,[status(thm)],[57])).
% 0.18/0.45 tff(123,plain,
% 0.18/0.45 (r2_hidden(k6_lattices(A!0), B!1)),
% 0.18/0.45 inference(and_elim,[status(thm)],[122])).
% 0.18/0.45 tff(124,plain,
% 0.18/0.45 (((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1)))) <=> ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | (~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(125,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | ((~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(126,plain,
% 0.18/0.45 ((~![A: $i, B: $i] : ((~v1_xboole_0(B)) | (~r2_hidden(A, B)))) | (~v1_xboole_0(B!1)) | (~r2_hidden(k6_lattices(A!0), B!1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.18/0.45 tff(127,plain,
% 0.18/0.45 (~v1_xboole_0(B!1)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[126, 123, 121])).
% 0.18/0.45 tff(128,plain,
% 0.18/0.45 (v14_lattices(A!0)),
% 0.18/0.45 inference(and_elim,[status(thm)],[122])).
% 0.18/0.45 tff(129,plain,
% 0.18/0.45 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(130,plain,
% 0.18/0.45 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1))) <=> (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(131,plain,
% 0.18/0.45 ((~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) <=> (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(132,plain,
% 0.18/0.45 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.45 tff(133,plain,
% 0.18/0.45 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1))) <=> (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[132, 130])).
% 0.18/0.45 tff(134,plain,
% 0.18/0.45 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[133])).
% 0.18/0.45 tff(135,plain,
% 0.18/0.45 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[134, 129])).
% 0.18/0.45 tff(136,plain,
% 0.18/0.45 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B!1)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(137,plain,
% 0.18/0.46 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B) = u1_struct_0(A!0))))) | (~v14_lattices(A!0)) | (~r2_hidden(k6_lattices(A!0), B)))) | v1_xboole_0(B!1) | (~r2_hidden(k6_lattices(A!0), B!1)) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.46 tff(138,plain,
% 0.18/0.46 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[137, 128, 123, 127, 111])).
% 0.18/0.46 tff(139,plain,
% 0.18/0.46 (~((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0))))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[138, 91])).
% 0.18/0.46 tff(140,plain,
% 0.18/0.46 (((~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), k17_filter_2(A!0))) | (~(k19_filter_2(A!0, B!1) = u1_struct_0(A!0)))) | (k19_filter_2(A!0, B!1) = u1_struct_0(A!0))),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(141,plain,
% 0.18/0.46 (k19_filter_2(A!0, B!1) = u1_struct_0(A!0)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.18/0.46 tff(142,plain,
% 0.18/0.46 (k19_filter_2(A!0, B!1) = k17_filter_2(A!0)),
% 0.18/0.46 inference(transitivity,[status(thm)],[141, 36])).
% 0.18/0.46 tff(143,plain,
% 0.18/0.46 (r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) <=> r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[142])).
% 0.18/0.46 tff(144,plain,
% 0.18/0.46 (m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[141])).
% 0.18/0.46 tff(145,plain,
% 0.18/0.46 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.46 inference(symmetry,[status(thm)],[144])).
% 0.18/0.46 tff(146,plain,
% 0.18/0.46 (m2_filter_2(u1_struct_0(A!0), A!0) <=> m2_filter_2(k17_filter_2(A!0), A!0)),
% 0.18/0.46 inference(monotonicity,[status(thm)],[36])).
% 0.18/0.46 tff(147,plain,
% 0.18/0.46 (m2_filter_2(k17_filter_2(A!0), A!0) <=> m2_filter_2(u1_struct_0(A!0), A!0)),
% 0.18/0.46 inference(symmetry,[status(thm)],[146])).
% 0.18/0.46 tff(148,plain,
% 0.18/0.46 (^[A: $i] : refl((m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(149,plain,
% 0.18/0.46 (![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[148])).
% 0.18/0.46 tff(150,plain,
% 0.18/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m2_filter_2(k17_filter_2(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(151,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> ![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[150])).
% 0.18/0.46 tff(152,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(153,plain,
% 0.18/0.46 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(154,plain,
% 0.18/0.46 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[153])).
% 0.18/0.46 tff(155,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m2_filter_2(k17_filter_2(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k17_filter_2')).
% 0.18/0.46 tff(156,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.18/0.46 tff(157,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.18/0.46 tff(158,plain,(
% 0.18/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(k17_filter_2(A), A))),
% 0.18/0.46 inference(skolemize,[status(sab)],[157])).
% 0.18/0.46 tff(159,plain,
% 0.18/0.46 (![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.18/0.46 tff(160,plain,
% 0.18/0.46 (![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[159, 149])).
% 0.18/0.46 tff(161,plain,
% 0.18/0.46 (((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))) <=> ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(162,plain,
% 0.18/0.46 ((m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(163,plain,
% 0.18/0.46 (((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0)))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[162])).
% 0.18/0.46 tff(164,plain,
% 0.18/0.46 (((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0))),
% 0.18/0.46 inference(transitivity,[status(thm)],[163, 161])).
% 0.18/0.46 tff(165,plain,
% 0.18/0.46 ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (m2_filter_2(k17_filter_2(A!0), A!0) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(166,plain,
% 0.18/0.46 ((~![A: $i] : (m2_filter_2(k17_filter_2(A), A) | v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k17_filter_2(A!0), A!0)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.46 tff(167,plain,
% 0.18/0.46 (m2_filter_2(k17_filter_2(A!0), A!0)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[166, 28, 27, 26, 160])).
% 0.18/0.46 tff(168,plain,
% 0.18/0.46 (m2_filter_2(u1_struct_0(A!0), A!0)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[167, 147])).
% 0.18/0.46 tff(169,plain,
% 0.18/0.46 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(170,plain,
% 0.18/0.46 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(171,plain,
% 0.18/0.46 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.18/0.46 tff(172,plain,
% 0.18/0.46 (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[171, 56, 168])).
% 0.18/0.46 tff(173,plain,
% 0.18/0.46 ((v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))) | m2_lattice4(u1_struct_0(A!0), A!0)),
% 0.18/0.46 inference(tautology,[status(thm)],[])).
% 0.18/0.46 tff(174,plain,
% 0.18/0.46 (m2_lattice4(u1_struct_0(A!0), A!0)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.18/0.46 tff(175,plain,
% 0.18/0.46 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(176,plain,
% 0.18/0.46 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(177,plain,
% 0.18/0.46 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.18/0.46 tff(178,plain,
% 0.18/0.46 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[177, 87, 174])).
% 0.18/0.46 tff(179,plain,
% 0.18/0.46 (m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[178, 145])).
% 0.18/0.46 tff(180,plain,
% 0.18/0.46 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(181,plain,
% 0.18/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.46 tff(182,plain,
% 0.18/0.46 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(183,plain,
% 0.18/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[182])).
% 0.18/0.46 tff(184,plain,
% 0.18/0.46 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(185,plain,
% 0.18/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[184])).
% 0.18/0.46 tff(186,plain,
% 0.18/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(transitivity,[status(thm)],[185, 183])).
% 0.18/0.46 tff(187,plain,
% 0.18/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(188,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[187])).
% 0.18/0.46 tff(189,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(190,plain,
% 0.18/0.46 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) <=> ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), (![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) <=> ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(191,plain,
% 0.18/0.46 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[190])).
% 0.18/0.46 tff(192,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t38_filter_2')).
% 0.18/0.46 tff(193,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.18/0.46 tff(194,plain,
% 0.18/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.18/0.46 tff(195,plain,(
% 0.18/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[194])).
% 0.18/0.47 tff(196,plain,
% 0.18/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.18/0.47 tff(197,plain,
% 0.18/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)) | (~v10_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[196, 186])).
% 0.18/0.47 tff(198,plain,
% 0.18/0.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[197, 181])).
% 0.18/0.47 tff(199,plain,
% 0.18/0.47 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(200,plain,
% 0.18/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(201,plain,
% 0.18/0.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, B), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.18/0.47 tff(202,plain,
% 0.18/0.47 (![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[201, 28, 27, 26, 198])).
% 0.18/0.47 tff(203,plain,
% 0.18/0.47 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | ((~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | (~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(204,plain,
% 0.18/0.47 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | ((~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(205,plain,
% 0.18/0.47 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B), B))) | (~m2_filter_2(B!1, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.18/0.47 tff(206,plain,
% 0.18/0.47 (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[205, 58, 202])).
% 0.18/0.47 tff(207,plain,
% 0.18/0.47 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(208,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[207])).
% 0.18/0.47 tff(209,plain,
% 0.18/0.47 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(210,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[209])).
% 0.18/0.47 tff(211,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(212,plain,
% 0.18/0.47 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(213,plain,
% 0.18/0.47 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[212])).
% 0.18/0.47 tff(214,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.18/0.47 tff(215,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.18/0.47 tff(216,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[215, 211])).
% 0.18/0.47 tff(217,plain,(
% 0.18/0.47 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[216])).
% 0.18/0.47 tff(218,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[217, 210])).
% 0.18/0.47 tff(219,plain,
% 0.18/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[218, 208])).
% 0.18/0.47 tff(220,plain,
% 0.18/0.47 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(221,plain,
% 0.18/0.47 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(222,plain,
% 0.18/0.47 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.18/0.47 tff(223,plain,
% 0.18/0.47 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[222, 26, 219])).
% 0.18/0.47 tff(224,plain,
% 0.18/0.47 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.18/0.47 inference(tautology,[status(thm)],[])).
% 0.18/0.47 tff(225,plain,
% 0.18/0.47 (l2_lattices(A!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.18/0.47 tff(226,plain,
% 0.18/0.47 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(227,plain,
% 0.18/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.18/0.47 tff(228,plain,
% 0.18/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(229,plain,
% 0.18/0.47 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(230,plain,
% 0.18/0.47 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[229])).
% 0.18/0.47 tff(231,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.18/0.47 tff(232,plain,
% 0.18/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.18/0.47 tff(233,plain,
% 0.18/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.18/0.47 tff(234,plain,(
% 0.18/0.47 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[233])).
% 0.18/0.47 tff(235,plain,
% 0.18/0.47 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.18/0.47 tff(236,plain,
% 0.18/0.47 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(237,plain,
% 0.18/0.47 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(238,plain,
% 0.18/0.47 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.18/0.47 tff(239,plain,
% 0.18/0.47 (l1_struct_0(A!0)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[238, 235, 225])).
% 0.18/0.47 tff(240,plain,
% 0.18/0.47 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(241,plain,
% 0.18/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[240])).
% 0.18/0.47 tff(242,plain,
% 0.18/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(243,plain,
% 0.18/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[242])).
% 0.18/0.47 tff(244,plain,
% 0.18/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(245,plain,
% 0.18/0.47 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(246,plain,
% 0.18/0.47 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[245])).
% 0.18/0.47 tff(247,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.18/0.47 tff(248,plain,
% 0.18/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.18/0.47 tff(249,plain,
% 0.18/0.47 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.18/0.47 tff(250,plain,(
% 0.18/0.47 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[249])).
% 0.18/0.47 tff(251,plain,
% 0.18/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.18/0.47 tff(252,plain,
% 0.18/0.47 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[251, 241])).
% 0.18/0.47 tff(253,plain,
% 0.18/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(254,plain,
% 0.18/0.47 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(255,plain,
% 0.18/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[254])).
% 0.18/0.47 tff(256,plain,
% 0.18/0.47 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[255, 253])).
% 0.18/0.47 tff(257,plain,
% 0.18/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(258,plain,
% 0.18/0.47 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.18/0.47 tff(259,plain,
% 0.18/0.47 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[258, 28, 252])).
% 0.18/0.47 tff(260,plain,
% 0.18/0.47 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[259, 239])).
% 0.18/0.47 tff(261,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(262,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[261])).
% 0.18/0.47 tff(263,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))))), rewrite((r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(264,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[263])).
% 0.18/0.47 tff(265,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(266,plain,
% 0.18/0.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), rewrite((r1_filter_2(A, B, C) => r1_filter_2(A, C, B)) <=> ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(267,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[266])).
% 0.18/0.47 tff(268,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','symmetry_r1_filter_2')).
% 0.18/0.47 tff(269,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.18/0.47 tff(270,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.18/0.47 tff(271,plain,(
% 0.18/0.47 ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 0.18/0.47 inference(skolemize,[status(sab)],[270])).
% 0.18/0.47 tff(272,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.18/0.47 tff(273,plain,
% 0.18/0.47 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[272, 262])).
% 0.18/0.47 tff(274,plain,
% 0.18/0.47 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(275,plain,
% 0.18/0.47 ((v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(276,plain,
% 0.18/0.47 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[275])).
% 0.18/0.47 tff(277,plain,
% 0.18/0.47 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[276, 274])).
% 0.18/0.48 tff(278,plain,
% 0.18/0.48 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(279,plain,
% 0.18/0.48 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.18/0.48 tff(280,plain,
% 0.18/0.48 (r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[279, 273, 260, 91, 206])).
% 0.18/0.48 tff(281,plain,
% 0.18/0.48 (r1_filter_2(u1_struct_0(A!0), B!1, k19_filter_2(A!0, B!1))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[280, 179])).
% 0.18/0.48 tff(282,plain,
% 0.18/0.48 (r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[281, 143])).
% 0.18/0.48 tff(283,plain,
% 0.18/0.48 ((u1_struct_0(A!0) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.18/0.48 inference(commutativity,[status(thm)],[])).
% 0.18/0.48 tff(284,plain,
% 0.18/0.48 ((k19_filter_2(A!0, B!1) = B!1) <=> (u1_struct_0(A!0) = B!1)),
% 0.18/0.48 inference(monotonicity,[status(thm)],[141])).
% 0.18/0.48 tff(285,plain,
% 0.18/0.48 ((k19_filter_2(A!0, B!1) = B!1) <=> (B!1 = u1_struct_0(A!0))),
% 0.18/0.48 inference(transitivity,[status(thm)],[284, 283])).
% 0.18/0.48 tff(286,plain,
% 0.18/0.48 (^[A: $i, B: $i, C: $i] : refl(((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(287,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[286])).
% 0.18/0.48 tff(288,plain,
% 0.18/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(289,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[288])).
% 0.18/0.48 tff(290,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(291,plain,
% 0.18/0.48 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(292,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[291])).
% 0.18/0.48 tff(293,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_filter_2')).
% 0.18/0.48 tff(294,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.18/0.48 tff(295,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[294, 290])).
% 0.18/0.48 tff(296,plain,(
% 0.18/0.48 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[295])).
% 0.18/0.48 tff(297,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[296, 289])).
% 0.18/0.48 tff(298,plain,
% 0.18/0.48 (![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[297, 287])).
% 0.18/0.48 tff(299,plain,
% 0.18/0.48 (((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))) <=> ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(300,plain,
% 0.18/0.48 (((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(301,plain,
% 0.18/0.48 (((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[300])).
% 0.18/0.48 tff(302,plain,
% 0.18/0.48 (((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[301, 299])).
% 0.18/0.48 tff(303,plain,
% 0.18/0.48 ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(304,plain,
% 0.18/0.48 ((~![A: $i, B: $i, C: $i] : ((r1_filter_2(A, B, C) <=> (B = C)) | v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.18/0.48 tff(305,plain,
% 0.18/0.48 ((~m1_subset_1(k19_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[304, 298, 260, 91])).
% 0.18/0.48 tff(306,plain,
% 0.18/0.48 (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[305, 179])).
% 0.18/0.48 tff(307,plain,
% 0.18/0.48 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))) | (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1)) | (k19_filter_2(A!0, B!1) = B!1)),
% 0.18/0.48 inference(tautology,[status(thm)],[])).
% 0.18/0.48 tff(308,plain,
% 0.18/0.48 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, B!1), B!1) <=> (k19_filter_2(A!0, B!1) = B!1))) | (k19_filter_2(A!0, B!1) = B!1)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[307, 206])).
% 0.18/0.48 tff(309,plain,
% 0.18/0.48 (k19_filter_2(A!0, B!1) = B!1),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[308, 306])).
% 0.18/0.48 tff(310,plain,
% 0.18/0.48 (B!1 = u1_struct_0(A!0)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[309, 285])).
% 0.18/0.48 tff(311,plain,
% 0.18/0.48 ((~(~((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0)))))) <=> ((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(312,plain,
% 0.18/0.48 ((r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0))) <=> (~((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(313,plain,
% 0.18/0.48 ((~(r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0)))) <=> (~(~((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[312])).
% 0.18/0.48 tff(314,plain,
% 0.18/0.48 ((~(r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0)))) <=> ((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[313, 311])).
% 0.18/0.48 tff(315,plain,
% 0.18/0.48 (~(r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0)) & (B!1 = u1_struct_0(A!0)))),
% 0.18/0.48 inference(or_elim,[status(thm)],[57])).
% 0.18/0.48 tff(316,plain,
% 0.18/0.48 ((~r1_filter_2(u1_struct_0(A!0), B!1, k17_filter_2(A!0))) | (~(B!1 = u1_struct_0(A!0)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.18/0.48 tff(317,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[316, 310, 282])).
% 0.18/0.48 % SZS output end Proof
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------