%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MSC010+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:17:32 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MSC010+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 23:32:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(leq_type, type, (
% 0.12/0.39 leq: ( $i * $i ) > $o)).
% 0.12/0.39 tff(n5_type, type, (
% 0.12/0.39 n5: $i)).
% 0.12/0.39 tff(n0_type, type, (
% 0.12/0.39 n0: $i)).
% 0.12/0.39 tff(init_type, type, (
% 0.12/0.39 init: $i)).
% 0.12/0.39 tff(a_select3_type, type, (
% 0.12/0.39 a_select3: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(q_ds1_filter_init_type, type, (
% 0.12/0.39 q_ds1_filter_init: $i)).
% 0.12/0.39 tff(id_ds1_filter_init_type, type, (
% 0.12/0.39 id_ds1_filter_init: $i)).
% 0.12/0.39 tff(pred_type, type, (
% 0.12/0.39 pred: $i > $i)).
% 0.12/0.39 tff(pv63_type, type, (
% 0.12/0.39 pv63: $i)).
% 0.12/0.39 tff(gt_type, type, (
% 0.12/0.39 gt: ( $i * $i ) > $o)).
% 0.12/0.39 tff(pv64_type, type, (
% 0.12/0.39 pv64: $i)).
% 0.12/0.39 tff(pminus_ds1_filter_init_type, type, (
% 0.12/0.39 pminus_ds1_filter_init: $i)).
% 0.12/0.39 tff(xhatmin_ds1_filter_init_type, type, (
% 0.12/0.39 xhatmin_ds1_filter_init: $i)).
% 0.12/0.39 tff(r_ds1_filter_init_type, type, (
% 0.12/0.39 r_ds1_filter_init: $i)).
% 0.12/0.39 tff(n2_type, type, (
% 0.12/0.39 n2: $i)).
% 0.12/0.39 tff(dv_ds1_filter_init_type, type, (
% 0.12/0.39 dv_ds1_filter_init: $i)).
% 0.12/0.39 tff(phi_ds1_filter_init_type, type, (
% 0.12/0.39 phi_ds1_filter_init: $i)).
% 0.12/0.39 tff(h_ds1_filter_init_type, type, (
% 0.12/0.39 h_ds1_filter_init: $i)).
% 0.12/0.39 tff(n998_type, type, (
% 0.12/0.39 n998: $i)).
% 0.12/0.39 tff(pv5_type, type, (
% 0.12/0.39 pv5: $i)).
% 0.12/0.39 tff(tptp_fun_X8_6_type, type, (
% 0.12/0.39 tptp_fun_X8_6: $i)).
% 0.12/0.39 tff(tptp_fun_X7_7_type, type, (
% 0.12/0.39 tptp_fun_X7_7: $i)).
% 0.12/0.39 tff(tptp_fun_X22_19_type, type, (
% 0.12/0.39 tptp_fun_X22_19: $i)).
% 0.12/0.39 tff(tptp_fun_X16_14_type, type, (
% 0.12/0.39 tptp_fun_X16_14: $i)).
% 0.12/0.39 tff(tptp_fun_X18_15_type, type, (
% 0.12/0.39 tptp_fun_X18_15: $i)).
% 0.12/0.39 tff(tptp_fun_X17_16_type, type, (
% 0.12/0.39 tptp_fun_X17_16: $i)).
% 0.12/0.39 tff(tptp_fun_X14_12_type, type, (
% 0.12/0.39 tptp_fun_X14_12: $i)).
% 0.12/0.39 tff(tptp_fun_X13_13_type, type, (
% 0.12/0.39 tptp_fun_X13_13: $i)).
% 0.12/0.39 tff(tptp_fun_X19_17_type, type, (
% 0.12/0.39 tptp_fun_X19_17: $i)).
% 0.12/0.39 tff(tptp_fun_X20_18_type, type, (
% 0.12/0.39 tptp_fun_X20_18: $i)).
% 0.12/0.39 tff(tptp_fun_X12_10_type, type, (
% 0.12/0.39 tptp_fun_X12_10: $i)).
% 0.12/0.39 tff(tptp_fun_X11_11_type, type, (
% 0.12/0.39 tptp_fun_X11_11: $i)).
% 0.12/0.39 tff(tptp_fun_X10_8_type, type, (
% 0.12/0.39 tptp_fun_X10_8: $i)).
% 0.12/0.39 tff(tptp_fun_X9_9_type, type, (
% 0.12/0.39 tptp_fun_X9_9: $i)).
% 0.12/0.39 tff(tptp_fun_X2_0_type, type, (
% 0.12/0.39 tptp_fun_X2_0: $i)).
% 0.12/0.39 tff(tptp_fun_X1_1_type, type, (
% 0.12/0.39 tptp_fun_X1_1: $i)).
% 0.12/0.39 tff(tptp_fun_X6_4_type, type, (
% 0.12/0.39 tptp_fun_X6_4: $i)).
% 0.12/0.39 tff(tptp_fun_X5_5_type, type, (
% 0.12/0.39 tptp_fun_X5_5: $i)).
% 0.12/0.39 tff(tptp_fun_X4_2_type, type, (
% 0.12/0.39 tptp_fun_X4_2: $i)).
% 0.12/0.39 tff(tptp_fun_X3_3_type, type, (
% 0.12/0.39 tptp_fun_X3_3: $i)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X7: $i, X8: $i] : refl(((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))) <=> ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X7: $i, X8: $i] : ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))) <=> ![X7: $i, X8: $i] : ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5)) <=> (~((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))))), ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) <=> (~(~((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))))))), rewrite((~(~((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))))) <=> ((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))), ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) <=> ((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))))), (((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> (((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)))), rewrite((((~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))), (((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ![X7: $i, X8: $i] : ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~(~(~((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init))))))) <=> (~((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,axiom,(~(~(~((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','n91')).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (~((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.41 ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[8])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))),
% 0.20/0.41 inference(and_elim,[status(thm)],[9])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.20/0.41 tff(12,plain,(
% 0.20/0.41 ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))),
% 0.20/0.41 inference(skolemize,[status(sab)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (![X7: $i, X8: $i] : ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (![X7: $i, X8: $i] : ((a_select3(q_ds1_filter_init, X7, X8) = init) | (~leq(n0, X7)) | (~leq(n0, X8)) | (~leq(X7, n5)) | (~leq(X8, n5)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 ((~((pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22!19, pv64)))) <=> (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 ((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) <=> (~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[8])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.41 tff(19,plain,(
% 0.20/0.41 ~((pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22!19, pv64)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[18])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (leq(X22!19, pv64)),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (~(a_select3(id_ds1_filter_init, pv63, X22!19) = init)),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (leq(X22!19, n5)),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (leq(n0, X22!19)),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (~(pv64 = X22!19)),
% 0.20/0.41 inference(or_elim,[status(thm)],[20])).
% 0.20/0.41 tff(26,assumption,(![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))), introduced(assumption)).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (leq(pv63, n5) <=> leq(pv63, n5)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (leq(pv63, n5)),
% 0.20/0.41 inference(and_elim,[status(thm)],[9])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (leq(pv63, n5)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (leq(n0, pv63) <=> leq(n0, pv63)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (leq(n0, pv63)),
% 0.20/0.41 inference(and_elim,[status(thm)],[9])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (leq(n0, pv63)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | ((~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64)))) <=> ((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (((pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22!19, pv64))) <=> ((~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | ((pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22!19, pv64)))) <=> ((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | ((~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | ((pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22!19, pv64)))) <=> ((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 ((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | ((pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22!19, pv64)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (pv64 = X22!19) | (~leq(n0, X22!19)) | (~leq(X22!19, n5)) | (a_select3(id_ds1_filter_init, pv63, X22!19) = init) | (~leq(X22!19, pv64))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[38, 32, 29, 26, 25, 24, 23, 22, 21])).
% 0.20/0.42 tff(40,plain,(~![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (^[X16: $i] : refl(((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) <=> ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,(
% 0.20/0.42 ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[45])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.42 tff(48,assumption,(~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))), introduced(assumption)).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)) | (~(a_select3(id_ds1_filter_init, pv63, X16!14) = init))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (~(a_select3(id_ds1_filter_init, pv63, X16!14) = init)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)) | leq(X16!14, n5)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (leq(X16!14, n5)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 48])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)) | leq(n0, X16!14)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (leq(n0, X16!14)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[53, 48])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)) | gt(pv64, X16!14)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 (gt(pv64, X16!14)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 48])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | ((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) <=> ((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) <=> ((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | ((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) <=> ((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | ((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | ((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) <=> ((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))),
% 0.20/0.42 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | ((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[62, 32, 29, 56, 54, 52, 50, 47])).
% 0.20/0.42 tff(64,plain,((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (^[X17: $i, X18: $i] : refl(((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17))) <=> ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17))) <=> ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (^[X17: $i, X18: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5)) <=> (~((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5))))), ((~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) <=> (~(~((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5))))))), rewrite((~(~((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5))))) <=> ((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)))), ((~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) <=> ((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5))))), (((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) <=> ((a_select3(id_ds1_filter_init, X17, X18) = init) | ((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5))) | (~gt(pv63, X17))))), rewrite(((a_select3(id_ds1_filter_init, X17, X18) = init) | ((~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5))) | (~gt(pv63, X17))) <=> ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))), (((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) <=> ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) <=> ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[67])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) <=> ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[9])).
% 0.20/0.42 tff(71,plain,
% 0.20/0.42 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,(
% 0.20/0.43 ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.43 tff(75,assumption,(~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))), introduced(assumption)).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))) | leq(X18!15, n5)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (leq(X18!15, n5)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))) | leq(X17!16, n5)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (leq(X17!16, n5)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))) | leq(n0, X18!15)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (leq(n0, X18!15)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))) | leq(n0, X17!16)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (leq(n0, X17!16)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 75])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))) | gt(pv63, X17!16)),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (gt(pv63, X17!16)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 75])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))) | (~(a_select3(id_ds1_filter_init, X17!16, X18!15) = init))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (~(a_select3(id_ds1_filter_init, X17!16, X18!15) = init)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[86, 75])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | ((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))) <=> ((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | (a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)) | (~gt(pv63, X17!16))) <=> ((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | ((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)) | (~gt(pv63, X17!16)))) <=> ((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | ((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[89])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | ((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)) | (~gt(pv63, X17!16)))) <=> ((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | (a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[90, 88])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | ((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)) | (~gt(pv63, X17!16)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ((~![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~leq(n0, X17)) | (~leq(n0, X18)) | (~leq(X17, n5)) | (~leq(X18, n5)) | (~gt(pv63, X17)))) | (a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[93, 87, 85, 83, 81, 79, 77, 74])).
% 0.20/0.43 tff(95,plain,((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (^[X13: $i, X14: $i] : refl(((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))) <=> ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))) <=> ![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 (^[X13: $i, X14: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5)) <=> (~((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))))), ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) <=> (~(~((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))))))), rewrite((~(~((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))))) <=> ((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))), ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) <=> ((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))))), (((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> (((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)))), rewrite((((~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))), (((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))),
% 0.20/0.44 inference(and_elim,[status(thm)],[9])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.44 tff(103,plain,(
% 0.20/0.44 ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))),
% 0.20/0.44 inference(skolemize,[status(sab)],[102])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.20/0.44 tff(106,assumption,(~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))), introduced(assumption)).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))) | leq(X14!12, n5)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (leq(X14!12, n5)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))) | leq(X13!13, n5)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (leq(X13!13, n5)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[109, 106])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))) | leq(n0, X14!12)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (leq(n0, X14!12)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))) | leq(n0, X13!13)),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (leq(n0, X13!13)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[113, 106])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))) | (~(a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (~(a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[115, 106])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (((~![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))) | ((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) <=> ((~![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((~![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))) | ((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 ((~![X13: $i, X14: $i] : ((a_select3(pminus_ds1_filter_init, X13, X14) = init) | (~leq(n0, X13)) | (~leq(n0, X14)) | (~leq(X13, n5)) | (~leq(X14, n5)))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[119, 116, 114, 112, 110, 108, 105])).
% 0.20/0.44 tff(121,plain,((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (^[X19: $i] : refl(((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (^[X19: $i] : rewrite(((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[125, 123])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (^[X19: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X19) & leq(X19, pred(pv63))) <=> (~((~leq(n0, X19)) | (~leq(X19, pred(pv63)))))), ((~(leq(n0, X19) & leq(X19, pred(pv63)))) <=> (~(~((~leq(n0, X19)) | (~leq(X19, pred(pv63)))))))), rewrite((~(~((~leq(n0, X19)) | (~leq(X19, pred(pv63)))))) <=> ((~leq(n0, X19)) | (~leq(X19, pred(pv63))))), ((~(leq(n0, X19) & leq(X19, pred(pv63)))) <=> ((~leq(n0, X19)) | (~leq(X19, pred(pv63)))))), quant_intro(proof_bind(^[X20: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X20) & leq(X20, n5)) <=> (~((~leq(n0, X20)) | (~leq(X20, n5))))), ((~(leq(n0, X20) & leq(X20, n5))) <=> (~(~((~leq(n0, X20)) | (~leq(X20, n5))))))), rewrite((~(~((~leq(n0, X20)) | (~leq(X20, n5))))) <=> ((~leq(n0, X20)) | (~leq(X20, n5)))), ((~(leq(n0, X20) & leq(X20, n5))) <=> ((~leq(n0, X20)) | (~leq(X20, n5))))), (((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)) <=> (((~leq(n0, X20)) | (~leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))), rewrite((((~leq(n0, X20)) | (~leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)) <=> ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))), (((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)) <=> ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))))), (![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)) <=> ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))), (((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> (((~leq(n0, X19)) | (~leq(X19, pred(pv63)))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))))), rewrite((((~leq(n0, X19)) | (~leq(X19, pred(pv63)))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))), (((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))),
% 0.20/0.44 inference(and_elim,[status(thm)],[9])).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.44 tff(132,plain,(
% 0.20/0.44 ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[131])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.45 tff(134,plain,
% 0.20/0.45 (![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.45 tff(135,assumption,(~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))), introduced(assumption)).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))) | leq(X19!17, pred(pv63))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 (leq(X19!17, pred(pv63))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 (((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))) | leq(n0, X19!17)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (leq(n0, X19!17)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | ((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init)))) <=> ((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19!17, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5)))) <=> ((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | ((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19!17, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) <=> ((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | ((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | ((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19!17, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) <=> ((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[142, 140])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 ((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | ((~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19!17, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~![X19: $i] : ((~leq(n0, X19)) | (~leq(X19, pred(pv63))) | ![X20: $i] : ((a_select3(id_ds1_filter_init, X19, X20) = init) | (~leq(n0, X20)) | (~leq(X20, n5))))) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))) | ![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[145, 139, 137, 134])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))) | leq(X20!18, n5)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (leq(X20!18, n5)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[147, 135])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))) | leq(n0, X20!18)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (leq(n0, X20!18)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[149, 135])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))) | (~(a_select3(id_ds1_filter_init, X19!17, X20!18) = init))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (~(a_select3(id_ds1_filter_init, X19!17, X20!18) = init)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[151, 135])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | ((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)))) <=> ((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (((~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)) <=> ((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | ((~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))) <=> ((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | ((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | ((~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))) <=> ((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[155, 153])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | ((~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 ((~![X20: $i] : ((~leq(n0, X20)) | (~leq(X20, n5)) | (a_select3(id_ds1_filter_init, X19!17, X20) = init))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[158, 152, 150, 148, 146])).
% 0.20/0.45 tff(160,plain,((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (^[X11: $i, X12: $i] : refl(((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))) <=> ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))) <=> ![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (^[X11: $i, X12: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0)) <=> (~((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))))), ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) <=> (~(~((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))))))), rewrite((~(~((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))))) <=> ((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))), ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) <=> ((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))))), (((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> (((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)))), rewrite((((~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))), (((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))),
% 0.20/0.45 inference(and_elim,[status(thm)],[9])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.20/0.45 tff(168,plain,(
% 0.20/0.45 ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))),
% 0.20/0.45 inference(skolemize,[status(sab)],[167])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.20/0.46 tff(171,assumption,(~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))), introduced(assumption)).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))) | leq(X12!10, n0)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (leq(X12!10, n0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.20/0.46 tff(174,plain,
% 0.20/0.46 (((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))) | leq(X11!11, n5)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (leq(X11!11, n5)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[174, 171])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))) | leq(n0, X12!10)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 (leq(n0, X12!10)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[176, 171])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))) | leq(n0, X11!11)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (leq(n0, X11!11)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[178, 171])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 (((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))) | (~(a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 (~(a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[180, 171])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 (((~![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))) | ((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) <=> ((~![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((~![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))) | ((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 ((~![X11: $i, X12: $i] : ((a_select3(xhatmin_ds1_filter_init, X11, X12) = init) | (~leq(n0, X11)) | (~leq(n0, X12)) | (~leq(X11, n5)) | (~leq(X12, n0)))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 181, 179, 177, 175, 173, 170])).
% 0.20/0.46 tff(186,plain,((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (^[X9: $i, X10: $i] : refl(((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))) <=> ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))) <=> ![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (^[X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2)) <=> (~((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))))), ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) <=> (~(~((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))))))), rewrite((~(~((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))))) <=> ((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))), ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) <=> ((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))))), (((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> (((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)))), rewrite((((~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))), (((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(190,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.46 tff(191,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(192,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))),
% 0.20/0.46 inference(and_elim,[status(thm)],[9])).
% 0.20/0.46 tff(193,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.46 tff(194,plain,(
% 0.20/0.46 ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))),
% 0.20/0.46 inference(skolemize,[status(sab)],[193])).
% 0.20/0.46 tff(195,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.20/0.46 tff(196,plain,
% 0.20/0.46 (![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.20/0.46 tff(197,assumption,(~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))), introduced(assumption)).
% 0.20/0.46 tff(198,plain,
% 0.20/0.46 (((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))) | leq(X10!8, n2)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(199,plain,
% 0.20/0.46 (leq(X10!8, n2)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.20/0.46 tff(200,plain,
% 0.20/0.47 (((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))) | leq(X9!9, n2)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(201,plain,
% 0.20/0.47 (leq(X9!9, n2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.20/0.47 tff(202,plain,
% 0.20/0.47 (((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))) | leq(n0, X10!8)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(203,plain,
% 0.20/0.47 (leq(n0, X10!8)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[202, 197])).
% 0.20/0.47 tff(204,plain,
% 0.20/0.47 (((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))) | leq(n0, X9!9)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(205,plain,
% 0.20/0.47 (leq(n0, X9!9)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[204, 197])).
% 0.20/0.47 tff(206,plain,
% 0.20/0.47 (((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))) | (~(a_select3(r_ds1_filter_init, X9!9, X10!8) = init))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(207,plain,
% 0.20/0.47 (~(a_select3(r_ds1_filter_init, X9!9, X10!8) = init)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[206, 197])).
% 0.20/0.47 tff(208,plain,
% 0.20/0.47 (((~![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))) | ((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) <=> ((~![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(209,plain,
% 0.20/0.47 ((~![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))) | ((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(210,plain,
% 0.20/0.47 ((~![X9: $i, X10: $i] : ((a_select3(r_ds1_filter_init, X9, X10) = init) | (~leq(n0, X9)) | (~leq(n0, X10)) | (~leq(X9, n2)) | (~leq(X10, n2)))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.20/0.47 tff(211,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[210, 207, 205, 203, 201, 199, 196])).
% 0.20/0.47 tff(212,plain,((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(213,plain,
% 0.20/0.47 (^[X1: $i, X2: $i] : refl(((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))) <=> ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(214,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))) <=> ![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.47 tff(215,plain,
% 0.20/0.47 (^[X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5)) <=> (~((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))))), ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) <=> (~(~((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))))))), rewrite((~(~((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))))) <=> ((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))), ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) <=> ((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))))), (((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> (((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))) | (a_select3(h_ds1_filter_init, X1, X2) = init)))), rewrite((((~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))), (((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(216,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[215])).
% 0.20/0.47 tff(217,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(218,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))),
% 0.20/0.47 inference(and_elim,[status(thm)],[9])).
% 0.20/0.47 tff(219,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.47 tff(220,plain,(
% 0.20/0.47 ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))),
% 0.20/0.47 inference(skolemize,[status(sab)],[219])).
% 0.20/0.47 tff(221,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.20/0.47 tff(222,plain,
% 0.20/0.47 (![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.20/0.47 tff(223,assumption,(~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))), introduced(assumption)).
% 0.20/0.47 tff(224,plain,
% 0.20/0.47 (((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))) | leq(X2!0, n5)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(225,plain,
% 0.20/0.47 (leq(X2!0, n5)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.20/0.47 tff(226,plain,
% 0.20/0.47 (((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))) | leq(X1!1, n2)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(227,plain,
% 0.20/0.47 (leq(X1!1, n2)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[226, 223])).
% 0.20/0.47 tff(228,plain,
% 0.20/0.47 (((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))) | (~(a_select3(h_ds1_filter_init, X1!1, X2!0) = init))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(229,plain,
% 0.20/0.47 (~(a_select3(h_ds1_filter_init, X1!1, X2!0) = init)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[228, 223])).
% 0.20/0.47 tff(230,plain,
% 0.20/0.47 (((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))) | leq(n0, X2!0)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(231,plain,
% 0.20/0.47 (leq(n0, X2!0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[230, 223])).
% 0.20/0.47 tff(232,plain,
% 0.20/0.47 (((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))) | leq(n0, X1!1)),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(233,plain,
% 0.20/0.47 (leq(n0, X1!1)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[232, 223])).
% 0.20/0.47 tff(234,plain,
% 0.20/0.47 (((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | ((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) <=> ((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(235,plain,
% 0.20/0.47 (((a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (~leq(X2!0, n5)) | (~leq(X1!1, n2))) <=> ((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(236,plain,
% 0.20/0.47 (((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | ((a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (~leq(X2!0, n5)) | (~leq(X1!1, n2)))) <=> ((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | ((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[235])).
% 0.20/0.47 tff(237,plain,
% 0.20/0.47 (((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | ((a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (~leq(X2!0, n5)) | (~leq(X1!1, n2)))) <=> ((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[236, 234])).
% 0.20/0.47 tff(238,plain,
% 0.20/0.47 ((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | ((a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (~leq(X2!0, n5)) | (~leq(X1!1, n2)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(239,plain,
% 0.20/0.47 ((~![X1: $i, X2: $i] : ((a_select3(h_ds1_filter_init, X1, X2) = init) | (~leq(n0, X1)) | (~leq(n0, X2)) | (~leq(X2, n5)) | (~leq(X1, n2)))) | (~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.20/0.47 tff(240,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[239, 233, 231, 229, 227, 225, 222])).
% 0.20/0.47 tff(241,plain,((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(242,plain,
% 0.20/0.47 (^[X5: $i, X6: $i] : refl(((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))) <=> ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(243,plain,
% 0.20/0.47 (![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))) <=> ![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[242])).
% 0.20/0.47 tff(244,plain,
% 0.20/0.47 (^[X5: $i, X6: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0)) <=> (~((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))))), ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) <=> (~(~((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))))))), rewrite((~(~((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))))) <=> ((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))), ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) <=> ((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))))), (((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> (((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)))), rewrite((((~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))), (((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(245,plain,
% 0.20/0.48 (![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[244])).
% 0.20/0.48 tff(246,plain,
% 0.20/0.48 (![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(247,plain,
% 0.20/0.48 (![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))),
% 0.20/0.48 inference(and_elim,[status(thm)],[9])).
% 0.20/0.48 tff(248,plain,
% 0.20/0.48 (![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.20/0.48 tff(249,plain,(
% 0.20/0.48 ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))),
% 0.20/0.48 inference(skolemize,[status(sab)],[248])).
% 0.20/0.48 tff(250,plain,
% 0.20/0.48 (![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.20/0.48 tff(251,plain,
% 0.20/0.48 (![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[250, 243])).
% 0.20/0.48 tff(252,assumption,(~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))), introduced(assumption)).
% 0.20/0.48 tff(253,plain,
% 0.20/0.48 (((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))) | leq(X6!4, n0)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(254,plain,
% 0.20/0.48 (leq(X6!4, n0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.20/0.48 tff(255,plain,
% 0.20/0.48 (((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))) | leq(X5!5, n5)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(256,plain,
% 0.20/0.48 (leq(X5!5, n5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[255, 252])).
% 0.20/0.48 tff(257,plain,
% 0.20/0.48 (((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))) | leq(n0, X6!4)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(258,plain,
% 0.20/0.48 (leq(n0, X6!4)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[257, 252])).
% 0.20/0.48 tff(259,plain,
% 0.20/0.48 (((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))) | leq(n0, X5!5)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(260,plain,
% 0.20/0.48 (leq(n0, X5!5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[259, 252])).
% 0.20/0.48 tff(261,plain,
% 0.20/0.48 (((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))) | (~(a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(262,plain,
% 0.20/0.48 (~(a_select3(dv_ds1_filter_init, X5!5, X6!4) = init)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[261, 252])).
% 0.20/0.48 tff(263,plain,
% 0.20/0.48 (((~![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))) | ((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) <=> ((~![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(264,plain,
% 0.20/0.48 ((~![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))) | ((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(265,plain,
% 0.20/0.48 ((~![X5: $i, X6: $i] : ((a_select3(dv_ds1_filter_init, X5, X6) = init) | (~leq(n0, X5)) | (~leq(n0, X6)) | (~leq(X5, n5)) | (~leq(X6, n0)))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.48 tff(266,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[265, 262, 260, 258, 256, 254, 251])).
% 0.20/0.48 tff(267,plain,((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(268,plain,
% 0.20/0.48 (^[X3: $i, X4: $i] : refl(((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))) <=> ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(269,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))) <=> ![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[268])).
% 0.20/0.48 tff(270,plain,
% 0.20/0.48 (^[X3: $i, X4: $i] : trans(monotonicity(trans(monotonicity(rewrite((leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5)) <=> (~((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))))), ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) <=> (~(~((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))))))), rewrite((~(~((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))))) <=> ((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))), ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) <=> ((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))))), (((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> (((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)))), rewrite((((~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))), (((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(271,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[270])).
% 0.20/0.48 tff(272,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(273,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))),
% 0.20/0.48 inference(and_elim,[status(thm)],[9])).
% 0.20/0.48 tff(274,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.48 tff(275,plain,(
% 0.20/0.48 ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))),
% 0.20/0.48 inference(skolemize,[status(sab)],[274])).
% 0.20/0.48 tff(276,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.20/0.48 tff(277,plain,
% 0.20/0.48 (![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[276, 269])).
% 0.20/0.48 tff(278,assumption,(~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))), introduced(assumption)).
% 0.20/0.48 tff(279,plain,
% 0.20/0.48 (((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))) | leq(n0, X4!2)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(280,plain,
% 0.20/0.48 (leq(n0, X4!2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[279, 278])).
% 0.20/0.48 tff(281,plain,
% 0.20/0.48 (((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))) | leq(n0, X3!3)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(282,plain,
% 0.20/0.48 (leq(n0, X3!3)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[281, 278])).
% 0.20/0.48 tff(283,plain,
% 0.20/0.48 (((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))) | leq(X4!2, n5)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(284,plain,
% 0.20/0.48 (leq(X4!2, n5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[283, 278])).
% 0.20/0.48 tff(285,plain,
% 0.20/0.48 (((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))) | leq(X3!3, n5)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(286,plain,
% 0.20/0.48 (leq(X3!3, n5)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[285, 278])).
% 0.20/0.48 tff(287,plain,
% 0.20/0.48 (((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))) | (~(a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(288,plain,
% 0.20/0.48 (~(a_select3(phi_ds1_filter_init, X3!3, X4!2) = init)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[287, 278])).
% 0.20/0.48 tff(289,plain,
% 0.20/0.48 (((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | ((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) <=> ((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)) | (~leq(X3!3, n5)) | (~leq(X4!2, n5))) <=> ((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 (((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | ((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)))) <=> ((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | ((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[290])).
% 0.20/0.49 tff(292,plain,
% 0.20/0.49 (((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | ((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)))) <=> ((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[291, 289])).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 ((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | ((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 ((~![X3: $i, X4: $i] : ((a_select3(phi_ds1_filter_init, X3, X4) = init) | (~leq(n0, X3)) | (~leq(n0, X4)) | (~leq(X3, n5)) | (~leq(X4, n5)))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[294, 288, 286, 284, 282, 280, 277])).
% 0.20/0.49 tff(296,plain,((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(297,plain,
% 0.20/0.49 ((~(pv63 = pv64)) <=> (~(pv63 = pv64))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 (~(pv63 = pv64)),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 (~(pv63 = pv64)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.49 tff(300,plain,
% 0.20/0.49 (leq(pv64, n5) <=> leq(pv64, n5)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 (leq(pv64, n5)),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 (leq(pv64, n5)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.20/0.49 tff(303,plain,
% 0.20/0.49 (leq(pv5, n998) <=> leq(pv5, n998)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 (leq(pv5, n998)),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 (leq(pv5, n998)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 (leq(n0, pv64) <=> leq(n0, pv64)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 (leq(n0, pv64)),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(308,plain,
% 0.20/0.49 (leq(n0, pv64)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.20/0.49 tff(309,plain,
% 0.20/0.49 (leq(n0, pv5) <=> leq(n0, pv5)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(310,plain,
% 0.20/0.49 (leq(n0, pv5)),
% 0.20/0.49 inference(and_elim,[status(thm)],[9])).
% 0.20/0.49 tff(311,plain,
% 0.20/0.49 (leq(n0, pv5)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.20/0.49 tff(312,plain,
% 0.20/0.49 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(313,plain,
% 0.20/0.49 ((~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))) <=> (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(314,plain,
% 0.20/0.49 ((~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) <=> (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(315,plain,
% 0.20/0.49 ((~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) <=> (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(316,plain,
% 0.20/0.49 ((~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) <=> (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(317,plain,
% 0.20/0.49 ((~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) <=> (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(318,plain,
% 0.20/0.49 ((~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) <=> (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(319,plain,
% 0.20/0.49 ((~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) <=> (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(320,plain,
% 0.20/0.49 ((~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) <=> (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(321,plain,
% 0.20/0.49 ((~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) <=> (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(322,plain,
% 0.20/0.49 ((~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) <=> (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(323,plain,
% 0.20/0.49 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[322, 321, 320, 319, 318, 317, 316, 315, 314, 313])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[323, 312])).
% 0.20/0.50 tff(325,plain,
% 0.20/0.50 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(327,plain,
% 0.20/0.51 ((leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5))))) <=> (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(328,plain,
% 0.20/0.51 ((~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))) <=> (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(329,plain,
% 0.20/0.51 ((leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))) <=> (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[328])).
% 0.20/0.51 tff(330,plain,
% 0.20/0.51 ((leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))) <=> (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63)))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[329, 327])).
% 0.20/0.51 tff(331,plain,
% 0.20/0.51 ((~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) <=> (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(332,plain,
% 0.20/0.51 ((~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) <=> (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(333,plain,
% 0.20/0.51 ((~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) <=> (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(334,plain,
% 0.20/0.51 ((~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) <=> (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(335,plain,
% 0.20/0.51 ((~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) <=> (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(336,plain,
% 0.20/0.51 ((~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) <=> (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(337,plain,
% 0.20/0.51 ((~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) <=> (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(338,plain,
% 0.20/0.51 ((~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) <=> (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(339,plain,
% 0.20/0.51 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[338, 337, 336, 335, 334, 333, 332, 331, 322, 330])).
% 0.20/0.51 tff(340,plain,
% 0.20/0.51 (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((~leq(n0, X1!1)) | (~leq(n0, X2!0)) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init) | (~leq(X1!1, n2)) | (~leq(X2!0, n5)))) | (~((a_select3(phi_ds1_filter_init, X3!3, X4!2) = init) | (~leq(X3!3, n5)) | (~leq(X4!2, n5)) | (~leq(n0, X3!3)) | (~leq(n0, X4!2)))) | (~((a_select3(dv_ds1_filter_init, X5!5, X6!4) = init) | (~leq(n0, X5!5)) | (~leq(n0, X6!4)) | (~leq(X5!5, n5)) | (~leq(X6!4, n0)))) | (~((a_select3(q_ds1_filter_init, X7!7, X8!6) = init) | (~leq(n0, X7!7)) | (~leq(n0, X8!6)) | (~leq(X7!7, n5)) | (~leq(X8!6, n5)))) | (~((a_select3(r_ds1_filter_init, X9!9, X10!8) = init) | (~leq(n0, X9!9)) | (~leq(n0, X10!8)) | (~leq(X9!9, n2)) | (~leq(X10!8, n2)))) | (~((a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init) | (~leq(n0, X11!11)) | (~leq(n0, X12!10)) | (~leq(X11!11, n5)) | (~leq(X12!10, n0)))) | (~((a_select3(id_ds1_filter_init, X19!17, X20!18) = init) | (~leq(n0, X20!18)) | (~leq(X20!18, n5)) | (~leq(n0, X19!17)) | (~leq(X19!17, pred(pv63))))) | (~((a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init) | (~leq(n0, X13!13)) | (~leq(n0, X14!12)) | (~leq(X13!13, n5)) | (~leq(X14!12, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~gt(pv63, X17!16)) | (~leq(n0, X17!16)) | (~leq(n0, X18!15)) | (~leq(X17!16, n5)) | (~leq(X18!15, n5)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[339, 326])).
% 0.20/0.52 tff(341,plain,
% 0.20/0.52 ((((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(342,plain,
% 0.20/0.52 (((pv63 = pv64) | (~leq(n0, pv5)) | (~leq(n0, pv63)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv63, n5)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(343,plain,
% 0.20/0.52 (((leq(n0, X19!17) & leq(X19!17, pred(pv63))) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))) <=> (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(344,plain,
% 0.20/0.52 ((~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) <=> (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(345,plain,
% 0.20/0.52 ((~((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) <=> (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(346,plain,
% 0.20/0.52 (((pv63 = pv64) | (~leq(n0, pv5)) | (~leq(n0, pv63)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv63, n5)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | ((leq(n0, X19!17) & leq(X19!17, pred(pv63))) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) <=> ((pv63 = pv64) | (~leq(n0, pv5)) | (~leq(n0, pv63)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv63, n5)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[345, 344, 343])).
% 0.20/0.52 tff(347,plain,
% 0.20/0.52 (((pv63 = pv64) | (~leq(n0, pv5)) | (~leq(n0, pv63)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv63, n5)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | ((leq(n0, X19!17) & leq(X19!17, pred(pv63))) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[346, 342])).
% 0.20/0.53 tff(348,plain,
% 0.20/0.53 ((((pv63 = pv64) | (~leq(n0, pv5)) | (~leq(n0, pv63)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv63, n5)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | ((leq(n0, X19!17) & leq(X19!17, pred(pv63))) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) <=> (((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[347])).
% 0.20/0.53 tff(349,plain,
% 0.20/0.53 ((((pv63 = pv64) | (~leq(n0, pv5)) | (~leq(n0, pv63)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv63, n5)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | ((leq(n0, X19!17) & leq(X19!17, pred(pv63))) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) <=> ((pv63 = pv64) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))) | (~leq(n0, pv5)) | (~leq(n0, pv64)) | (~leq(pv5, n998)) | (~leq(pv64, n5)) | (~((~(leq(n0, X1!1) & leq(n0, X2!0) & leq(X1!1, n2) & leq(X2!0, n5))) | (a_select3(h_ds1_filter_init, X1!1, X2!0) = init))) | (~((~(leq(n0, X3!3) & leq(n0, X4!2) & leq(X3!3, n5) & leq(X4!2, n5))) | (a_select3(phi_ds1_filter_init, X3!3, X4!2) = init))) | (~((~(leq(n0, X5!5) & leq(n0, X6!4) & leq(X5!5, n5) & leq(X6!4, n0))) | (a_select3(dv_ds1_filter_init, X5!5, X6!4) = init))) | (~((~(leq(n0, X7!7) & leq(n0, X8!6) & leq(X7!7, n5) & leq(X8!6, n5))) | (a_select3(q_ds1_filter_init, X7!7, X8!6) = init))) | (~((~(leq(n0, X9!9) & leq(n0, X10!8) & leq(X9!9, n2) & leq(X10!8, n2))) | (a_select3(r_ds1_filter_init, X9!9, X10!8) = init))) | (~((~(leq(n0, X11!11) & leq(n0, X12!10) & leq(X11!11, n5) & leq(X12!10, n0))) | (a_select3(xhatmin_ds1_filter_init, X11!11, X12!10) = init))) | (~((~(leq(n0, X13!13) & leq(n0, X14!12) & leq(X13!13, n5) & leq(X14!12, n5))) | (a_select3(pminus_ds1_filter_init, X13!13, X14!12) = init))) | (~((a_select3(id_ds1_filter_init, X17!16, X18!15) = init) | (~(leq(n0, X17!16) & leq(n0, X18!15) & leq(X17!16, n5) & leq(X18!15, n5))) | (~gt(pv63, X17!16)))) | (~((~leq(n0, pv63)) | (~leq(pv63, n5)) | (~gt(pv64, X16!14)) | (~leq(n0, X16!14)) | (~leq(X16!14, n5)) | (a_select3(id_ds1_filter_init, pv63, X16!14) = init))) | (leq(n0, X19!17) & leq(X19!17, pred(pv63)) & (~((~(leq(n0, X20!18) & leq(X20!18, n5))) | (a_select3(id_ds1_filter_init, X19!17, X20!18) = init)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[348, 341])).
% 0.20/0.53 tff(350,plain,
% 0.20/0.53 (((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) <=> ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(351,plain,
% 0.20/0.53 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))) <=> ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(352,plain,
% 0.20/0.53 (^[X22: $i] : rewrite(((~leq(X22, pv64)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(X22, n5)) | (pv64 = X22) | (~leq(n0, pv63)) | (~leq(n0, X22)) | (~leq(pv63, n5))) <=> ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(353,plain,
% 0.20/0.54 (![X22: $i] : ((~leq(X22, pv64)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(X22, n5)) | (pv64 = X22) | (~leq(n0, pv63)) | (~leq(n0, X22)) | (~leq(pv63, n5))) <=> ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[352])).
% 0.20/0.54 tff(354,plain,
% 0.20/0.54 (![X21: $i, X22: $i] : ((~leq(X22, pv64)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(X22, n5)) | (pv64 = X22) | (~leq(n0, pv63)) | (~leq(n0, X22)) | (~leq(pv63, n5))) <=> ![X22: $i] : ((~leq(X22, pv64)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(X22, n5)) | (pv64 = X22) | (~leq(n0, pv63)) | (~leq(n0, X22)) | (~leq(pv63, n5)))),
% 0.20/0.54 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.54 tff(355,plain,
% 0.20/0.54 (![X21: $i, X22: $i] : ((a_select3(id_ds1_filter_init, X21, X22) = init) | (~(leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))) | (~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64)))) <=> ![X21: $i, X22: $i] : ((~leq(X22, pv64)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(X22, n5)) | (pv64 = X22) | (~leq(n0, pv63)) | (~leq(n0, X22)) | (~leq(pv63, n5)))),
% 0.20/0.54 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.54 tff(356,plain,
% 0.20/0.54 (![X21: $i, X22: $i] : ((a_select3(id_ds1_filter_init, X21, X22) = init) | (~(leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))) | (~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64)))) <=> ![X22: $i] : ((~leq(X22, pv64)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(X22, n5)) | (pv64 = X22) | (~leq(n0, pv63)) | (~leq(n0, X22)) | (~leq(pv63, n5)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[355, 354])).
% 0.20/0.54 tff(357,plain,
% 0.20/0.54 (![X21: $i, X22: $i] : ((a_select3(id_ds1_filter_init, X21, X22) = init) | (~(leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))) | (~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64)))) <=> ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[356, 353])).
% 0.20/0.54 tff(358,plain,
% 0.20/0.54 (^[X21: $i, X22: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) <=> (leq(n0, X21) & leq(n0, X22) & leq(X21, n5))), ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) <=> ((leq(n0, X21) & leq(n0, X22) & leq(X21, n5)) & leq(X22, n5)))), rewrite(((leq(n0, X21) & leq(n0, X22) & leq(X21, n5)) & leq(X22, n5)) <=> (leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))), ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) <=> (leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5)))), trans(monotonicity(rewrite((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) <=> ((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))), (((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)) <=> (((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)))), rewrite((((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)) <=> ((~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))) | (a_select3(id_ds1_filter_init, X21, X22) = init))), (((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)) <=> ((~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))) | (a_select3(id_ds1_filter_init, X21, X22) = init)))), (((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init))) <=> ((leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5)) => ((~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))) | (a_select3(id_ds1_filter_init, X21, X22) = init))))), rewrite(((leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5)) => ((~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))) | (a_select3(id_ds1_filter_init, X21, X22) = init))) <=> ((a_select3(id_ds1_filter_init, X21, X22) = init) | (~(leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))) | (~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))))), (((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init))) <=> ((a_select3(id_ds1_filter_init, X21, X22) = init) | (~(leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))) | (~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(359,plain,
% 0.20/0.54 (![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init))) <=> ![X21: $i, X22: $i] : ((a_select3(id_ds1_filter_init, X21, X22) = init) | (~(leq(n0, X21) & leq(n0, X22) & leq(X21, n5) & leq(X22, n5))) | (~((~(pv64 = X22)) & (X21 = pv63) & leq(X22, pv64))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[358])).
% 0.20/0.54 tff(360,plain,
% 0.20/0.54 (![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init))) <=> ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[359, 357])).
% 0.20/0.54 tff(361,plain,
% 0.20/0.54 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(362,plain,
% 0.20/0.54 (^[X19: $i] : trans(monotonicity(quant_intro(proof_bind(^[X20: $i] : rewrite(((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)) <=> ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))), (![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)) <=> ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))), (((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))), rewrite(((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))), (((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(363,plain,
% 0.20/0.54 (![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init))) <=> ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[362])).
% 0.20/0.54 tff(364,plain,
% 0.20/0.54 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(365,plain,
% 0.20/0.54 (^[X17: $i, X18: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) <=> (leq(n0, X17) & leq(n0, X18) & leq(X17, n5))), ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) <=> ((leq(n0, X17) & leq(n0, X18) & leq(X17, n5)) & leq(X18, n5)))), rewrite(((leq(n0, X17) & leq(n0, X18) & leq(X17, n5)) & leq(X18, n5)) <=> (leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))), ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) <=> (leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5)))), rewrite((gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)) <=> ((~gt(pv63, X17)) | (a_select3(id_ds1_filter_init, X17, X18) = init))), (((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init))) <=> ((leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5)) => ((~gt(pv63, X17)) | (a_select3(id_ds1_filter_init, X17, X18) = init))))), rewrite(((leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5)) => ((~gt(pv63, X17)) | (a_select3(id_ds1_filter_init, X17, X18) = init))) <=> ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))), (((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init))) <=> ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(366,plain,
% 0.20/0.54 (![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init))) <=> ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[365])).
% 0.20/0.54 tff(367,plain,
% 0.20/0.54 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(368,plain,
% 0.20/0.55 (^[X16: $i] : rewrite(((~gt(pv64, X16)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(X16, n5)) | (~leq(n0, pv63)) | (~leq(n0, X16)) | (~leq(pv63, n5))) <=> ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(369,plain,
% 0.20/0.55 (![X16: $i] : ((~gt(pv64, X16)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(X16, n5)) | (~leq(n0, pv63)) | (~leq(n0, X16)) | (~leq(pv63, n5))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[368])).
% 0.20/0.55 tff(370,plain,
% 0.20/0.55 (![X15: $i, X16: $i] : ((~gt(pv64, X16)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(X16, n5)) | (~leq(n0, pv63)) | (~leq(n0, X16)) | (~leq(pv63, n5))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(X16, n5)) | (~leq(n0, pv63)) | (~leq(n0, X16)) | (~leq(pv63, n5)))),
% 0.20/0.55 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.55 tff(371,plain,
% 0.20/0.55 (![X15: $i, X16: $i] : ((a_select3(id_ds1_filter_init, X15, X16) = init) | (~(leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))) | (~((X15 = pv63) & gt(pv64, X16)))) <=> ![X15: $i, X16: $i] : ((~gt(pv64, X16)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(X16, n5)) | (~leq(n0, pv63)) | (~leq(n0, X16)) | (~leq(pv63, n5)))),
% 0.20/0.55 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.55 tff(372,plain,
% 0.20/0.55 (![X15: $i, X16: $i] : ((a_select3(id_ds1_filter_init, X15, X16) = init) | (~(leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))) | (~((X15 = pv63) & gt(pv64, X16)))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(X16, n5)) | (~leq(n0, pv63)) | (~leq(n0, X16)) | (~leq(pv63, n5)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[371, 370])).
% 0.20/0.55 tff(373,plain,
% 0.20/0.55 (![X15: $i, X16: $i] : ((a_select3(id_ds1_filter_init, X15, X16) = init) | (~(leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))) | (~((X15 = pv63) & gt(pv64, X16)))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[372, 369])).
% 0.20/0.55 tff(374,plain,
% 0.20/0.55 (^[X15: $i, X16: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) <=> (leq(n0, X15) & leq(n0, X16) & leq(X15, n5))), ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) <=> ((leq(n0, X15) & leq(n0, X16) & leq(X15, n5)) & leq(X16, n5)))), rewrite(((leq(n0, X15) & leq(n0, X16) & leq(X15, n5)) & leq(X16, n5)) <=> (leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))), ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) <=> (leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5)))), rewrite((((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)) <=> ((~((X15 = pv63) & gt(pv64, X16))) | (a_select3(id_ds1_filter_init, X15, X16) = init))), (((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init))) <=> ((leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5)) => ((~((X15 = pv63) & gt(pv64, X16))) | (a_select3(id_ds1_filter_init, X15, X16) = init))))), rewrite(((leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5)) => ((~((X15 = pv63) & gt(pv64, X16))) | (a_select3(id_ds1_filter_init, X15, X16) = init))) <=> ((a_select3(id_ds1_filter_init, X15, X16) = init) | (~(leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))) | (~((X15 = pv63) & gt(pv64, X16))))), (((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init))) <=> ((a_select3(id_ds1_filter_init, X15, X16) = init) | (~(leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))) | (~((X15 = pv63) & gt(pv64, X16))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(375,plain,
% 0.20/0.55 (![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init))) <=> ![X15: $i, X16: $i] : ((a_select3(id_ds1_filter_init, X15, X16) = init) | (~(leq(n0, X15) & leq(n0, X16) & leq(X15, n5) & leq(X16, n5))) | (~((X15 = pv63) & gt(pv64, X16))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[374])).
% 0.20/0.55 tff(376,plain,
% 0.20/0.55 (![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init))) <=> ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[375, 373])).
% 0.20/0.55 tff(377,plain,
% 0.20/0.55 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(378,plain,
% 0.20/0.55 (^[X13: $i, X14: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) <=> (leq(n0, X13) & leq(n0, X14) & leq(X13, n5))), ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) <=> ((leq(n0, X13) & leq(n0, X14) & leq(X13, n5)) & leq(X14, n5)))), rewrite(((leq(n0, X13) & leq(n0, X14) & leq(X13, n5)) & leq(X14, n5)) <=> (leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))), ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) <=> (leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5)))), (((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ((leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init)))), rewrite(((leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))), (((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(379,plain,
% 0.20/0.55 (![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init)) <=> ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[378])).
% 0.20/0.55 tff(380,plain,
% 0.20/0.55 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(381,plain,
% 0.20/0.55 (^[X11: $i, X12: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) <=> (leq(n0, X11) & leq(n0, X12) & leq(X11, n5))), ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) <=> ((leq(n0, X11) & leq(n0, X12) & leq(X11, n5)) & leq(X12, n0)))), rewrite(((leq(n0, X11) & leq(n0, X12) & leq(X11, n5)) & leq(X12, n0)) <=> (leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))), ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) <=> (leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0)))), (((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ((leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)))), rewrite(((leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))), (((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(382,plain,
% 0.20/0.55 (![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) <=> ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[381])).
% 0.20/0.55 tff(383,plain,
% 0.20/0.55 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(384,plain,
% 0.20/0.55 (^[X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) <=> (leq(n0, X9) & leq(n0, X10) & leq(X9, n2))), ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) <=> ((leq(n0, X9) & leq(n0, X10) & leq(X9, n2)) & leq(X10, n2)))), rewrite(((leq(n0, X9) & leq(n0, X10) & leq(X9, n2)) & leq(X10, n2)) <=> (leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))), ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) <=> (leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2)))), (((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ((leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init)))), rewrite(((leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))), (((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(385,plain,
% 0.20/0.56 (![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init)) <=> ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[384])).
% 0.20/0.56 tff(386,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(387,plain,
% 0.20/0.56 (^[X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) <=> (leq(n0, X7) & leq(n0, X8) & leq(X7, n5))), ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) <=> ((leq(n0, X7) & leq(n0, X8) & leq(X7, n5)) & leq(X8, n5)))), rewrite(((leq(n0, X7) & leq(n0, X8) & leq(X7, n5)) & leq(X8, n5)) <=> (leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))), ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) <=> (leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5)))), (((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ((leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init)))), rewrite(((leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))), (((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(388,plain,
% 0.20/0.56 (![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init)) <=> ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[387])).
% 0.20/0.56 tff(389,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(390,plain,
% 0.20/0.56 (^[X5: $i, X6: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) <=> (leq(n0, X5) & leq(n0, X6) & leq(X5, n5))), ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) <=> ((leq(n0, X5) & leq(n0, X6) & leq(X5, n5)) & leq(X6, n0)))), rewrite(((leq(n0, X5) & leq(n0, X6) & leq(X5, n5)) & leq(X6, n0)) <=> (leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))), ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) <=> (leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0)))), (((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ((leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init)))), rewrite(((leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))), (((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(391,plain,
% 0.20/0.56 (![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init)) <=> ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[390])).
% 0.20/0.56 tff(392,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(393,plain,
% 0.20/0.56 (^[X3: $i, X4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) <=> (leq(n0, X3) & leq(n0, X4) & leq(X3, n5))), ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) <=> ((leq(n0, X3) & leq(n0, X4) & leq(X3, n5)) & leq(X4, n5)))), rewrite(((leq(n0, X3) & leq(n0, X4) & leq(X3, n5)) & leq(X4, n5)) <=> (leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))), ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) <=> (leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5)))), (((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ((leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init)))), rewrite(((leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))), (((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(394,plain,
% 0.20/0.56 (![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init)) <=> ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[393])).
% 0.20/0.56 tff(395,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(396,plain,
% 0.20/0.56 (^[X1: $i, X2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) <=> (leq(n0, X1) & leq(n0, X2) & leq(X1, n2))), ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) <=> ((leq(n0, X1) & leq(n0, X2) & leq(X1, n2)) & leq(X2, n5)))), rewrite(((leq(n0, X1) & leq(n0, X2) & leq(X1, n2)) & leq(X2, n5)) <=> (leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))), ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) <=> (leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5)))), (((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ((leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init)))), rewrite(((leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))), (((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(397,plain,
% 0.20/0.56 (![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init)) <=> ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[396])).
% 0.20/0.56 tff(398,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5)) & leq(pv64, n5)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(399,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998)) & leq(pv63, n5)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(400,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64)) & leq(pv5, n998)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(401,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63)) & leq(n0, pv64)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(402,plain,
% 0.20/0.56 ((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(403,plain,
% 0.20/0.56 (((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63)) & leq(n0, pv64))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[402])).
% 0.20/0.56 tff(404,plain,
% 0.20/0.56 (((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64))),
% 0.20/0.56 inference(transitivity,[status(thm)],[403, 401])).
% 0.20/0.56 tff(405,plain,
% 0.20/0.56 ((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64)) & leq(pv5, n998))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[404])).
% 0.20/0.56 tff(406,plain,
% 0.20/0.56 ((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998))),
% 0.20/0.56 inference(transitivity,[status(thm)],[405, 400])).
% 0.20/0.56 tff(407,plain,
% 0.20/0.56 (((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998)) & leq(pv63, n5))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[406])).
% 0.20/0.56 tff(408,plain,
% 0.20/0.56 (((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5))),
% 0.20/0.56 inference(transitivity,[status(thm)],[407, 399])).
% 0.20/0.56 tff(409,plain,
% 0.20/0.56 ((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5)) & leq(pv64, n5))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[408])).
% 0.20/0.56 tff(410,plain,
% 0.20/0.56 ((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5))),
% 0.20/0.56 inference(transitivity,[status(thm)],[409, 398])).
% 0.20/0.56 tff(411,plain,
% 0.20/0.56 (((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[410, 397])).
% 0.20/0.56 tff(412,plain,
% 0.20/0.56 (((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)))),
% 0.20/0.56 inference(transitivity,[status(thm)],[411, 395])).
% 0.20/0.56 tff(413,plain,
% 0.20/0.56 ((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[412, 394])).
% 0.20/0.57 tff(414,plain,
% 0.20/0.57 ((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[413, 392])).
% 0.20/0.57 tff(415,plain,
% 0.20/0.57 (((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[414, 391])).
% 0.20/0.57 tff(416,plain,
% 0.20/0.57 (((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[415, 389])).
% 0.20/0.57 tff(417,plain,
% 0.20/0.57 ((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[416, 388])).
% 0.20/0.57 tff(418,plain,
% 0.20/0.57 ((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[417, 386])).
% 0.20/0.57 tff(419,plain,
% 0.20/0.57 (((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[418, 385])).
% 0.20/0.57 tff(420,plain,
% 0.20/0.57 (((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)))),
% 0.20/0.57 inference(transitivity,[status(thm)],[419, 383])).
% 0.20/0.57 tff(421,plain,
% 0.20/0.57 ((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[420, 382])).
% 0.20/0.57 tff(422,plain,
% 0.20/0.57 ((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)))),
% 0.20/0.58 inference(transitivity,[status(thm)],[421, 380])).
% 0.20/0.58 tff(423,plain,
% 0.20/0.58 (((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[422, 379])).
% 0.20/0.58 tff(424,plain,
% 0.20/0.58 (((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)))),
% 0.20/0.58 inference(transitivity,[status(thm)],[423, 377])).
% 0.20/0.58 tff(425,plain,
% 0.20/0.58 ((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[424, 376])).
% 0.20/0.58 tff(426,plain,
% 0.20/0.58 ((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[425, 367])).
% 0.20/0.58 tff(427,plain,
% 0.20/0.58 (((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[426, 366])).
% 0.20/0.58 tff(428,plain,
% 0.20/0.58 (((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[427, 364])).
% 0.20/0.59 tff(429,plain,
% 0.20/0.59 ((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17)))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[428, 363])).
% 0.20/0.59 tff(430,plain,
% 0.20/0.59 ((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) <=> ((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[429, 361])).
% 0.20/0.59 tff(431,plain,
% 0.20/0.59 (((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)))) <=> (((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[430, 360])).
% 0.20/0.59 tff(432,plain,
% 0.20/0.59 (((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)))) <=> ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[431, 351])).
% 0.43/0.59 tff(433,axiom,((((((((((((((((((~(pv63 = pv64)) & leq(n0, pv5)) & leq(n0, pv63)) & leq(n0, pv64)) & leq(pv5, n998)) & leq(pv63, n5)) & leq(pv64, n5)) & ![X1: $i, X2: $i] : ((((leq(n0, X1) & leq(n0, X2)) & leq(X1, n2)) & leq(X2, n5)) => (a_select3(h_ds1_filter_init, X1, X2) = init))) & ![X3: $i, X4: $i] : ((((leq(n0, X3) & leq(n0, X4)) & leq(X3, n5)) & leq(X4, n5)) => (a_select3(phi_ds1_filter_init, X3, X4) = init))) & ![X5: $i, X6: $i] : ((((leq(n0, X5) & leq(n0, X6)) & leq(X5, n5)) & leq(X6, n0)) => (a_select3(dv_ds1_filter_init, X5, X6) = init))) & ![X7: $i, X8: $i] : ((((leq(n0, X7) & leq(n0, X8)) & leq(X7, n5)) & leq(X8, n5)) => (a_select3(q_ds1_filter_init, X7, X8) = init))) & ![X9: $i, X10: $i] : ((((leq(n0, X9) & leq(n0, X10)) & leq(X9, n2)) & leq(X10, n2)) => (a_select3(r_ds1_filter_init, X9, X10) = init))) & ![X11: $i, X12: $i] : ((((leq(n0, X11) & leq(n0, X12)) & leq(X11, n5)) & leq(X12, n0)) => (a_select3(xhatmin_ds1_filter_init, X11, X12) = init))) & ![X13: $i, X14: $i] : ((((leq(n0, X13) & leq(n0, X14)) & leq(X13, n5)) & leq(X14, n5)) => (a_select3(pminus_ds1_filter_init, X13, X14) = init))) & ![X15: $i, X16: $i] : ((((leq(n0, X15) & leq(n0, X16)) & leq(X15, n5)) & leq(X16, n5)) => (((X15 = pv63) & gt(pv64, X16)) => (a_select3(id_ds1_filter_init, X15, X16) = init)))) & ![X17: $i, X18: $i] : ((((leq(n0, X17) & leq(n0, X18)) & leq(X17, n5)) & leq(X18, n5)) => (gt(pv63, X17) => (a_select3(id_ds1_filter_init, X17, X18) = init)))) & ![X19: $i] : ((leq(n0, X19) & leq(X19, pred(pv63))) => ![X20: $i] : ((leq(n0, X20) & leq(X20, n5)) => (a_select3(id_ds1_filter_init, X19, X20) = init)))) => ![X21: $i, X22: $i] : ((((leq(n0, X21) & leq(n0, X22)) & leq(X21, n5)) & leq(X22, n5)) => ((((~(pv64 = X22)) & (X21 = pv63)) & leq(X22, pv64)) => (a_select3(id_ds1_filter_init, X21, X22) = init)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','n1')).
% 0.43/0.59 tff(434,plain,
% 0.43/0.59 ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.43/0.60 tff(435,plain,
% 0.43/0.60 ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[434, 350])).
% 0.43/0.60 tff(436,plain,
% 0.43/0.60 ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[435, 350])).
% 0.43/0.60 tff(437,plain,
% 0.43/0.60 ((~((~(pv63 = pv64)) & leq(n0, pv5) & leq(n0, pv63) & leq(n0, pv64) & leq(pv5, n998) & leq(pv63, n5) & leq(pv64, n5) & ![X1: $i, X2: $i] : ((~(leq(n0, X1) & leq(n0, X2) & leq(X1, n2) & leq(X2, n5))) | (a_select3(h_ds1_filter_init, X1, X2) = init)) & ![X3: $i, X4: $i] : ((~(leq(n0, X3) & leq(n0, X4) & leq(X3, n5) & leq(X4, n5))) | (a_select3(phi_ds1_filter_init, X3, X4) = init)) & ![X5: $i, X6: $i] : ((~(leq(n0, X5) & leq(n0, X6) & leq(X5, n5) & leq(X6, n0))) | (a_select3(dv_ds1_filter_init, X5, X6) = init)) & ![X7: $i, X8: $i] : ((~(leq(n0, X7) & leq(n0, X8) & leq(X7, n5) & leq(X8, n5))) | (a_select3(q_ds1_filter_init, X7, X8) = init)) & ![X9: $i, X10: $i] : ((~(leq(n0, X9) & leq(n0, X10) & leq(X9, n2) & leq(X10, n2))) | (a_select3(r_ds1_filter_init, X9, X10) = init)) & ![X11: $i, X12: $i] : ((~(leq(n0, X11) & leq(n0, X12) & leq(X11, n5) & leq(X12, n0))) | (a_select3(xhatmin_ds1_filter_init, X11, X12) = init)) & ![X13: $i, X14: $i] : ((~(leq(n0, X13) & leq(n0, X14) & leq(X13, n5) & leq(X14, n5))) | (a_select3(pminus_ds1_filter_init, X13, X14) = init)) & ![X16: $i] : ((~gt(pv64, X16)) | (~leq(n0, X16)) | (~leq(X16, n5)) | (a_select3(id_ds1_filter_init, pv63, X16) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5))) & ![X17: $i, X18: $i] : ((a_select3(id_ds1_filter_init, X17, X18) = init) | (~(leq(n0, X17) & leq(n0, X18) & leq(X17, n5) & leq(X18, n5))) | (~gt(pv63, X17))) & ![X19: $i] : ((~(leq(n0, X19) & leq(X19, pred(pv63)))) | ![X20: $i] : ((~(leq(n0, X20) & leq(X20, n5))) | (a_select3(id_ds1_filter_init, X19, X20) = init))))) | ![X22: $i] : ((pv64 = X22) | (~leq(n0, X22)) | (~leq(X22, n5)) | (a_select3(id_ds1_filter_init, pv63, X22) = init) | (~leq(n0, pv63)) | (~leq(pv63, n5)) | (~leq(X22, pv64)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[436, 350])).
% 0.43/0.60 Proof display could not be completed: monotonicity rule is not handled
% 0.43/0.60 % E exiting
%------------------------------------------------------------------------------